[EM] Quotaless STV-PR suggestion
On 07/02/2013 07:09 PM, Chris Benham wrote: I am sure this meets Droop Proportionality for Solid Coalitions. Kristofer Munsterhjelm wrote (3 July 2013): Does that mean that the method reduces to largest remainders Droop when the voters vote for all candidates of a single party each? Kristopher, Yes. STV meets Later-no-Harm because lower preferences only count after the the fate (elected or definitely eliminated) of more preferred candidates has been set. My suggestion doesn't because by not truncating a voter could have their ballot count towards the election of a non-favourite in an early round (and a candidate that might have won anyway), and so be reduced in weight and then not be heavy enough to elect the voter's favourite in a later round (when it would have been if the voter had truncated). Some STV fans might not like that, but I'm not fully on board with the LNHarm religion. While I think a very strong truncation incentive is a bad thing, absolute compliance with LNHarm makes it more likely that the result will (at least partly) be determined by the weak, maybe ill-informed, preferences of voters who are only really interested in their favourites (and certainly wouldn't have turned out if their favourites weren't on the ballot); thereby reducing the Social Utility of the full set of winners (and maybe compromising the legitimacy of some of them). I like IRV, but its compliance with LNHarm isn't IMO one of its best features. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Quotaless STV-PR suggestion
I'd like to propose an STV-like PR method that does without a quota. Here is the procedure for filling 3 seats: *Voters rank from the top however many candidates they wish. To fill the first seat, one-at-time 'eliminate' the candidate highest-ranked (among remaining candidates) on the fewest ballots until 4 candidates remain. The candidate A that is then top-ranked on the highest number of ballots is elected. A is dropped from the ballots and the 'eliminated' candidates are restored. Ballots that contributed to A's winning tally are now given a weight of 2 and all the other ballots a weight of 3. To fill the second seat, one-at-a-time 'eliminate' the candidate that is highest ranked on the smallest total weight of ballots until 3 candidates remain. The candidate B that is then highest ranked on the greatest total weight of ballots is elected. B is dropped from the ballots and previously 'eliminated' candidates are restored. Ballots that contributed to both A's and B's winning tallies are given a weight of 1. Ballots that contributed to the winning tally of a single candidate (A or B) are given a weight of 2. All the other ballots are given a weight of 3. To fill the final seat, one-at-a-time eliminate the candidate that is highest ranked on the smallest total weight of ballots until 2 remain. The candidate C that is then highest ranked on the greatest total weight of ballots is elected.* So initially each ballot is given a weight that is equal to the number of seats to be filled, and then they reduce in weight by 1 for each candidate they've helped elect. The number of candidates the field is reduced to in each round is equal to the numbers of seats not-yet-filled plus 1. I am sure this meets Droop Proportionality for Solid Coalitions. At least some versions of STV-PR have the problem that adding or removing a few ballots that vote for nobody (say just plump for some X that is ignored or voted no higher than equal-bottom on all the other ballots) can change at least one of the winners by changing the size of the quota. It is much simpler than Meek to explain and operate, but seems (from some examples I've seen) to give Meek-like results. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Preferential voting system where a candidate may win multiple seats
Kristopher Munsterhjelm wrote (30 June 2013): Would you suggest that the elimination ordering only be calculated based on the votes of those who currently don't get any representation? No, because that is only provisional. You'd have to go back to using quotas for that to be maybe ok. So votes tied up in the quotas of definitely elected candidates have no other say in who is elected or eliminated. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Preferential voting system where a candidate may win multiple seats
Kristofer Munsterhjelm wrote (29 June 2013): The combined method would go like this: 1. Run the ballots through RP (or Schulze, etc). Reverse the outcome ordering (or the ballots; these systems are reversal symmetric so it doesn't matter). Call the result the elimination order. 2. Distribute seats using Sainte-Laguë. 3. Call parties that receive no seats unrepresented. If there are unrepresented parties, remove the unrepresented party that is listed first in the elimination order. 4. Go to 2 until no party is unrepresented. This should help preserve parties that are popular as second preferences but not as first preferences, because the elimination order will remove parties that hide the second preferences before it removes the party that is being hidden, thus letting the second-preference party grow in support before it is at risk of being eliminated. Note that this doesn't solve the small-council problem. If we have: 46: L C R 44: R C L 10: C R L 1 seat, then the first seat goes to L just like in Plurality. The elimination order never enters the picture. Kristopher, I don't see this. Your elimination order is obviously L, R,C. R and C are unrepresented so we eliminate R. Then we have 46: L 54: C Then we redistribute the seat to C and then eliminate L and confirm the final redistribution. But I'm not on board with the spirit of this method, because it seems to give a say to voters who are efficiently represented a say in which party/candidate will represent other voters. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] MAV on electowiki
Jameson, ...But I don't think it's realistic... I don't think any of the multiple majorities scenarios are very realistic. Irrespective of how they are resolved, all voters who regard one or more of the viable candidates as unacceptable will have a strong incentive to top-rate all the candidates they regard as acceptable, out of fear that an unacceptable candidate gets a majority before their vote can help all the acceptable ones. I still say that your suggestion only increases that incentive (even though maybe more psychologically than likely to cause extra actual post-election regret). Forget about using the mechanism for resolving the (probably very rare) multiple-majorities scenario to try to gain some whiff of later-no-harm. BTW, the Majority Choice Approval Bucklin-like method using ratings (or grading) ballots, simply elected the candidate whose majority tally was the biggest. I also prefer that to your suggestion. It and yours are simpler to count than the Mike Ossipoff idea I support. I'm very glad to hear you think IBIFA is a great method. I'll stop quibbling about how you classify it. Condorcet is too complex. Does that mean that you don't care that it fails FBC?Condorcet//Approval is pretty simple (and IMO quite good). Am I right in assuming that you only like methods that meet FBC or Condorcet and maybe Mono-raise? And/or are biased towards electing centrists? And for some or all of these reasons you don't like IRV? Chris Benham Jameson Quinn wrote (27 June 2013): 2013/6/27 Chris Benham cbenha...@yahoo.com.au Jameson, I don't see it... Say on an ABCD grading ballot you give your Lesser Evil X a B, and then in the second round both X and your Greater Evil Y reach the majority threshold. In that case you obviously might have cause to regret that you didn't give X an A. OK, I see what you're saying now. But I don't think it's realistic. If X and Y both reach a majority at B, then there are some voters giving both of them a B or above. This looks a lot more like a chicken dilemma situation between two similar frontrunners, than like a situation where X versus Y is a gaping difference which justifies the use of a just-in-case strategy for a low-probability occurrence. Especially because, in a chicken dilemma situation, multiple majorities would tend to slide down towards the second-to-bottom rating, not up at the second-to-top one. That is why your suggestion makes it (even) less safe to not simply give all the acceptable candidates an A. I think that's [IBIFA] a great method, but I would classify it as improved Condorcet rather than Bucklin-like. No. There isn't any pairwise component in the algorithm, and unlike the Improved Condorcet methods it doesn't directly aim to come as close as possible to meeting Condorcet without violating Favorite Betrayal. There is no pairwise component in the narrowest sense, but it still is only summable at (R-1)*(N²), which is actually worse than a regular Condorcet method. Again, I think this method would deliver excellent results, and I see why it is in certain ways akin to a Bucklin or median method. But its quasi-pairwise counting complexity still makes me see it as more similar to improved Condorcet methods than to Bucklin ones. But another method I support is in that category, TTPBA//TR. Mike Ossipoff promoted it as Improved Condorcet, Top (or ICT). http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-January/029577.html Right, there's a lot of good methods out there. Any of these would satisfy me as more resistant to strategy than either Condorcet or Score. And those two in turn are quite satisfactory as being at least as good as approval with more expressivity, and approval is satisfactory as being a giant and strict improvement over plurality. Great. And I like to talk about the relative merits of each proposal here on the list. But if we talk like this in front of non-mathematical voters, we'll only turn them off. We need simple proposals. Approval is step one; most of us agree on that. But some voters, like Bruce Gilson, will never be satisfied with approval because it doesn't feel expressive enough. So I think it's worth having a second option to offer. To me, pitching Score feels dishonest: Look at this great system! Amazing great things it can do! (But watch out, if you vote other than approval-style, you'll probably regret it.) Condorcet is too complex. I want a simple, good system. MAV would fit the bill. If you have another proposal that would, then the way to get me onto your side is to demonstrate that it has more supporters than just you. That goes for you, Chris, and also for you, Abd. Jameson Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Preferential voting system where a candidate may win multiple seats
Vidar Wahlberg wrote (28 June 2013): I'm sticking to quota election because I don't fully grasp how to apply other methods (Sainte-Laguë, for instance) to determine when to start excluding parties. Vidar, Here is a hopefully clearer rewording of my suggestion: *Use the best formula for apportioning seats in List PR (based on first preference votes) to provisionally apportion the seats. If this apportionment gives every party at least one seat, confirm this apportionment as final. Otherwise, eliminate the party voted top on the fewest ballots and transfer that party's second-preference votes IRV-style. Based on the updated tallies (that include votes transferred from the eliminated party) again make a provisional apportionment. If that apportionment gives every uneliminated party at least one seat, then confirm it as final. Otherwise, again eliminate the party with the smallest vote tally (that might include votes from the already eliminated candidate) and again transfer votes IRV-style to uneliminated parties. Keep repeating this process until an apportionment is confirmed as final (when every uneliminated party has at least one seat).* I hope that is now clear. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Preferential voting system where a candidate may win multiple seats
Vidar, I'm a bit confused about the details of the method you say is used in Norway. You write that voters may rank parties in a preferred order instead of only being able to vote for a single party. but further down you refer to the one person, one vote system. Since you are not attempting to do anything with surpluses, I don't see any point in using a quota at all. I suggest instead simply: *Use the best formula for apportioning seats in List PR (based on first preference votes). If every list/party has at least one seat, finish. Otherwise, eliminate the party voted top on the fewest ballots and promote the next most preferred uneliminated candidate on those ballots to top. (In other words transfer the vote, Alternative Vote/IRV style). Based on the updated tallies (that include votes transferred from eliminated parties) repeat until the final apportionment leaves no party without a seat.* I think some free-riding incentive in PR is unavoidable. Not using a quota and distributing surpluses might reduce proportionality a bit among sincere coalitions, but doing so allows parties (whose voters only care about their favourites and are happy to take how-to-vote advice from them) doing cynical preference-swap deals, motivated by nothing but increasing the chance that they will get an extra seat (by having the biggest surplus fraction of a quota). I hope that helps. Chris Benham Vidar Wahlberg wrote (26 June 2013): Greetings! I'm new here, I'm not a mathematician and merely a layman on the subject of voting methods so please grant me some leeway, but do feel free to correct any misconceptions I may have. Briefly about my goals: I'm trying to find a better alternative to the voting system used in Norway (party-list PR, counting votes using a modified Sainte-Laguë method where first divisor is 1.4 instead of 1), where you still vote for parties rather than persons and may rank parties in a preferred order instead of only being able to vote for a single party. A party may win multiple seats in each district. The short answer to why not vote directly for persons? would be that in Norway there's more focus on the goals of a party rather than the goal of its politicians, and some may argue that the extra abstraction layer is a good thing, as well as I'd like an alternative that won't be completely alien to the common people. I'm hoping that any discussion that may arise won't focus on this aspect, though. As of why I'm interested in this then that's because I'm arguing for a preferential election rather than the one person one vote system which I believe is leading us towards a two/three party system, and I need to know (better) what options are out there. So far I've not been able to find much information on preferential voting system where you vote for a party rather than a person. If anyone have more insight and can guide me to more literature I would appreciate it. And here's the part where I hope you'll be gentle: I tinkered a bit on my own. Where as I am a fan of Ranked Pairs and Beatpath, I find those difficult to explain to someone with no insight in voting systems, and neither could I figure out how to apply RP in a way where a candidate can win multiple seats. The basics behind PR-STV on the other hand are fairly easy to explain, and I did manage to implement a way of counting votes to candidates which can win multiple seats based on the ideas behind STV, but I'm no expert on voting methods and would like to hear your thoughts. This is the general approach: 1. Calculate quota (Droop): votes / (seats + 1) + 1 2. Tally votes, assign seats to candidates with enough votes to exceed the quota [1]: candidate.seats = candidate.votes / quota 3. Calculate new vote weight: vote.weight = vote.weight - candidate.seats * quota / candidate.votes 4. Exclude candidate with least votes and redistribute those votes [2] 5. Repeat step 2-4 until all but one candidate has been excluded (which gets the final seat) [1]: Since a candidate is not excluded from further seat allocations upon reaching the quota the surplus votes are not redistributed. I do not know which adverse effects this may have that are not present in STV where candidates are excluded upon reaching the quota. [2]: It troubles me to decide which candidate that should be considered to have the fewer votes. If I choose the one with fewest first preference votes, then I may exclude a candidate that is very popular as a second choice, while a candidate that is popular by a few and despised by many may stay longer in the election. Since votes to elected candidates are not distributed to secondary preference then this issue is likely elevated. I'm contemplating on rather excluding the candidate that is least common on any ballot, regardless of rank, but I'm not certain on the implications this would cause. Since a candidate may win multiple seats, it should be more difficult to use Hylland free
[EM] MAV on electowiki
Jameson, I don't see it... Say on an ABCD grading ballot you give your Lesser Evil X a B, and then in the second round both X and your Greater Evil Y reach the majority threshold. In that case you obviously might have cause to regret that you didn't give X an A. That is why your suggestion makes it (even) less safe to not simply give all the acceptable candidates an A. I think that's [IBIFA] a great method, but I would classify it as improved Condorcet rather than Bucklin-like. No. There isn't any pairwise component in the algorithm, and unlike the Improved Condorcet methods it doesn't directly aim to come as close as possible to meeting Condorcet without violating Favorite Betrayal. But another method I support is in that category, TTPBA//TR. Mike Ossipoff promoted it as Improved Condorcet, Top (or ICT). http://lists.electorama.com/pipermail/election-methods-electorama.com/2012-January/029577.html Chris Benham Jameson Quinn wrote (27 June 2013): 2013/6/26 Chris Benham cbenha...@yahoo.com.au Jameson, I don't like this version at all. These methods all have the problem that the voters have a strong incentive to just submit approval ballots, i.e. only use the top and bottom grades. You are right... if they believe that all other voters will act the same way. But if experience has shown that there are enough honest voters so that winning medians¹ tend to be in a given range, then it is safe to vote expressively outside that range. ¹ Actually, as long as your vote for your preferred frontrunner is above the second-place median, and your vote for your less-preferred frontrunner is below the first-place median, your vote is strategically optimal. Your suggested way of determining a winner among candidates who first get a majority in the same round only makes that incentive a bit stronger still. I don't see it. The MAV completion method is as close to later-no-harm as is possible in a Bucklin system; which tends to balance out the later-no-help. I think you're the one who's pointed out before that passing one and failing the other is usually worse than failing both; by the same token, if one is passed by all Bucklin systems, then the Bucklin system which fails the other by the least is the best. I agree with a Mike Ossipoff suggestion, that we elect the member of that set of candidates with the most above-bottom votes. That completion is fine. My larger point is that it's silly to fight about these issues. We should settle on one Bucklin proposal and stick to it. I currently believe that MAV is most viable in that sense, but I'd be happy if you got enough support for the Ossipoff suggestion to convince me otherwise. Also, given the strong truncation incentive, I think 5 grades is one too many. In my opinion 4 grades would be adequately expressive. I personally slightly prefer 5 grades. It increases the probability that a voter who wants to be strategic and confidently knows the expected range of possible winning (and second-place) medians, will have room to make purely-expressive distinctions at the top and/or bottom of the ballot. In other words, if you know that the winner always gets a C, then it is strategically safe to make honest distinctions between A/B or between D/F. But that's a slight preference. If demonstrate that your position has more support among the active posters here, I'd join with you for the sake of unity. My favourite Bucklin-like method is Irrelevant-Ballot Independent Fallback-Approval (aka IBFA) that I introduced in May 2010. http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html I think that's a great method, but I would classify it as improved Condorcet rather than Bucklin-like. I think it would be productive to do the same work for the improved Condorcet systems that I'm trying to do with Bucklin: that is, to settle on a single simple proposal that people can agree is among the better options (even if they can't agree it's best), and find a simple descriptive name for that proposal. I expect IBIFA would be a strong contender in that process. It's possible that in the future, Bucklin and Improved Condorcet advocates could agree to join forces, but I suspect it's premature for that at the moment. If you disagree with the above, I'd be interested to hear how you see it. Jameson Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Preferential voting system where a candidate may win multiple seats
Vidar wrote: If I'm not to use a quota, but rather something like Sainte-Laguë as it's done today, how would I know when to start excluding the smaller parties? When one (or more) of them doesn't have a seat according to the initial (trial) apportionment. *Use the best formula for apportioning seats in List PR (based on first preference votes). If every list/party has at least one seat, finish. Otherwise, eliminate the party voted top on the fewest ballots and promote the next most preferred uneliminated candidate on those ballots to top. (In other words transfer the vote, Alternative Vote/IRV style). Based on the updated tallies (that include votes transferred from eliminated parties) repeat until the final apportionment leaves no party without a seat.* As for eliminating the party voted top on fewest ballots, that does seem to have a weakness I'm trying to mend. For example, take the following votes: 7 A,B,E,C,D 9 C,B,D,E,A 6 B,D,E,A,C Here B would be eliminated first, even though B is popular among all these voters, where as A and C are popular among fewer voters. I believe Ranked Pairs Beatpath would rank B above A C in this scenario. This is why I'm contemplating on rather eliminating the candidates that are least represented on the ballots regardless of rank, and rather fall back to eliminate the candidate with least first preference votes if there are multiple candidates least represented on ballots. I'm not entirely certain of the implications of such a change, though. And for it to have any effect, you would have to limit the amount of preferences instead of listing all candidates as I did in the example above. I think it is desirable that voters are free to rank as many candidates as they wish. My suggestion is simpler and meets the Later-no-Harm criterion. The problem you allude to I am sure would affect very few seats. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] MAV on electowiki
Jameson, I don't like this version at all. These methods all have the problem that the voters have a strong incentive to just submit approval ballots, i.e. only use the top and bottom grades. Your suggested way of determining a winner among candidates who first get a majority in the same round only makes that incentive a bit stronger still. I agree with a Mike Ossipoff suggestion, that we elect the member of that set of candidates with the most above-bottom votes. Also, given the strong truncation incentive, I think 5 grades is one too many. In my opinion 4 grades would be adequately expressive. My favourite Bucklin-like method is Irrelevant-Ballot Independent Fallback-Approval (aka IBFA) that I introduced in May 2010. http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html A, B, C, D are probably better names for the ratings slots than the Top, Middle1, Middle2, Bottom in that post. Comparing it to Bucklin, it meets Independence from Irrelevant Ballots which means that adding or removing a few ballots that bullet-vote for nobody (ignored on all the other ballots) can't change the winner. The small price paid for this (apart from greater complexity) is that it fails Later-no-Help. That is mostly a benefit because it weakens the truncation incentive. The other advantage of IBIFA over Bucklin is that it is far more likely to elect the Condorcet winner. If the winners are different then the IBIFA winner will always pairwise beat the Bucklin (or Majority Judgement) winner. Chris Benham Jameson Quinn wrote (19 June 2013): Here's the current version of the article. Note the new paragraph on strategy at the bottom. - Majority Approval Voting (MAV) is a modern, evaluativehttp://wiki.electorama.com/wiki/Evaluative version of Bucklin voting http://wiki.electorama.com/wiki/Bucklin_voting. Voters rate each candidate into one of a predefined set of ratings or grades, such as the letter grades A, B, C, D, and F. As with any Bucklin system, first the top-grade (A) votes for each candidate are counted as approvals. If one or more candidate has a majority, then the highest majority wins. If not, votes at next grade down (B) are added to each candidate's approval scores. If there are one or more candidates with a majority, the winner is whichever of those had more votes at higher grades (the previous stage). If there were no majorities, then the next grade down(C) is added and the process repeats; and so on. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Question about the Plurality Criterion
Ben, MinMax(Margins) fails the Plurality criterion. It elects the candidate with the weakest pairwise loss as measured by the difference between the two candidates' vote tallies. An alternative definition is that it elects the candidate who needs the fewest number of extra bullet-votes to be able to pairwise-beat all the other candidates. 3:A 5:BA 6:C CB 6-5, BA 5-3, AC 8-6. That method elects B, but the Plurality criterion says that B can't win because of C. Given that if the B voters had truncated the winner would have been C, this is also a failure of the Later-no-Help criterion. The method meets the Condorcet criterion and Mono-add-Top. It has been promoted here by Juho Laatu. Chris Benham Ben grant wrote (24 June 2013): As I have had it explained to me, the Plurality Criterion is: If there are two candidates X and Y so that X has more first place votes than Y has any place votes, then Y shouldn't win. Which I think means that if X has, for example, 100 votes, then B would have to appear on less than 100 ballots and still *win* for this criterion to be failed, yes? I cannot imagine a (halfway desirable) voting system that would fail the Plurality Criterion - can anyone tell me the simplest one that would? Apart from a lame one like least votes win, I mean? Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Score Voting and Approval Voting not practically substantially different from Plurality?
Ben Grant wrote: - Approval Voting tends to result in irrelevant approval votes being given to weak candidates – which is pointless, or slightly stronger (but still losing) candidates can once again present a spoiler effect where a person’s least preferred choice is elected because they cast their approval only toward their most preferred choice, who was nowhere near supported enough to stop their least preferred choice. Am I substantially wrong about any of this? Ultimately, in real and practical terms, it seems that done intelligently, Score Voting devolves into Approval Voting, and Approval Voting devolves into Plurality Voting. The idea is that some voters dislike feeling strategically pressured to vote their sincere favourites below equal-top. With voters never needing to vote their sincere favourites below equal-top, previous elections become a much better indicator of which candidates are really weak. So I don't see compliance with the Favorite Betrayal Criterion as pointless. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?
Oops! Yes, thanks Abd. I made an error. The A and B group was supposed to add up to 49, not 51. So it should be: 25: AYX 24: BYX 17: CDX 17: EFX 17: GHX 100 ballots, Bucklin election. The majority threshold is 51 and X wins in the third round. But if we add anywhere between 3 and 100 XY ballots then Y wins in the second round. Chris Benham At 03:58 PM 6/17/2013, Chris Benham wrote: Benjamin, The criterion (criteria is the plural) you suggest is not new. It is called Mono-add-Top, and comes from Douglas Woodall. It is met by IRV and MinMax(Margins) but is failed by Bucklin. In my opinion IRV is the best of the methods that meet it. 26: AYX 25: BYX 17: CDX 17: EFX 17: GHX The majority threshold is 51 and X wins in the third round. But if we add anywhere between 3 and 100 XY ballots then Y wins in the second round. Some error there. Total votes are 102. Majority is 52 votes. snip Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Participation Criteria and Bucklin - perhaps they *can* work together after all?
Benjamin, The criterion (criteria is the plural) you suggest is not new. It is called Mono-add-Top, and comes from Douglas Woodall. It is met by IRV and MinMax(Margins) but is failed by Bucklin. In my opinion IRV is the best of the methods that meet it. 26: AYX 25: BYX 17: CDX 17: EFX 17: GHX The majority threshold is 51 and X wins in the third round. But if we add anywhere between 3 and 100 XY ballots then Y wins in the second round. You'll find some interesting stuff on Kevin Venzke's old page: http://nodesiege.tripod.com/elections/ Notice that your version (in an earlier post) of the Plurality criterion is wrong. Chris Benham Benjamin Grant wrote (17 June 2013): OK, let's assume that as defined, Bucklin fails Participation. Let me specify a new criteria, which already either has its own name that I do not know, or which I can call Prime Participation: Adding one or more ballots that vote X as a highest preference should never change the winner from X to Y In other words, expressing a first place/greatest magnitude preference for X, if X was already winning, cannot make X not win. This may be another one so basic that few or maybe no real voting systems fail it? -Benn Grant eFix Computer Consulting mailto:benn at 4efix.com benn at 4efix.com 603.283.6601 Election-Methods mailing list - see http://electorama.com/em for list info
[EM] A better 2-round method that uses approval ballots
I just want to repeat a suggestion I've made here more than once. Take my previous example where the Centre-Right candidate is elected due to some of the Left candidate's supporters using the Compromise strategy. 49: Right 28: Centre-Right (7 are sincere LeftCentre-Right) 23: Left Centre-Right beats Right in the runoff 51-49. But the Right supporters have an easy Push-over strategy to (from their perspective) rectify this. If anywhere between 6 and *all* of them change their vote to approving both of Right and Left, then Left will be dragged back into the runoff with Right and then be beaten. My suggested 2-round method using Approval ballots is to elect the most approved first-round candidate A if A is approved on more than half the ballots, otherwise elect the winner of a runoff between A and the candidate that is most approved on ballots that don't show approval for A. This destroys the incentive for parties to field 2 candidates, and greatly reduces the Push-over incentive (to about the same as in normal plurality-ballot Top-2 Runoff). Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Does Top Two Approval fail the Favorite Betrayal Criterion [?]
Yes. Say there are three candidates: Right, Centre-Right and Left, and the approval votes cast are 49: Right 21: Centre-Right (all prefer Right to Left) 23: Left 07: Left, Centre-Right (sincere favourite is Left) Approval votes: Right 49, Left 30, Centre-Right 28. The top-2 runoff is between Right and Left and Right wins 70-30. All the voters who approved Left prefer Centre-Right to Right. The 7 voters who approved both Left and Centre-Right can change the winner to Centre-Right by dumping Left (their sincere favourite) in the first round. 49: Right 28: Centre-Right 23: Left Now the top-2 runoff is between Right and Centre-Right and Centre-Right wins 51-49. Seven voters have succeeded with a Compromise strategy. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Losing Votes (ERABW)
Kristofer Munsterhjelm wrote (13 Dec 2012): The method should provide good results and/or strategy resistance and then whether or not it pays attention to the top is secondary. Which leads to marketing. Perhaps having the method elect most from the tops is a marketing advantage. However, it may come at a cost of results (or strategy resistance). In that case, what is better? Should one pick a method for marketability and try to build upon it to go further later, or try to make one leap instead of two? I agree with the first sentence above, but good results can be a bit subjective and some people think that paying attention to the top is part of it. When I wrote that my suggested version of Schulze (Losing Votes) has a feature that might help with marketing, I wasn't admitting that anything in terms of results (or strategy resisatnce) had been sacrificed for greater marketability. With regard to strategy resistance in Condorcet methods, it seems that we have to choose between trying to reduce Compromise incentive for voters whose main concern is to prevent the election of their Greater Evil and trying to reduce defection incentive by voters trying to get their Favourite elected versus the sincere CW. The Losing Votes method I advocate goes for the latter. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Losing Votes (ERABW)
I recently proposed (16 Nov 2012) the Losing Votes (Equal-Ranking Above-Bottom Whole) method: *Voters rank from the top however many candidates they wish. Equal-ranking is allowed. The result is determined from a pairwise matrix. On that matrix, ballots that rank above bottom any X=Y contribute one whole vote to XY and another to YX. Ballots that truncate both X and Y have no effect on the XY and YX entries in the pairwise matrix. With the thus created pairwise matrix, decide the winner with Schulze (Losing Votes).* 35 A 10 A=B 30 BC 25 C AB 35-30 (ignoring the 10 A=B ballots unlike my proposal, according to which AB 45-40) BC 40-25 CA 55-45 (This is an old example from Kevin Venke in a different discussion.) B is pairwise beaten and positionally dominated by A and is the least approved (ranked above bottom) candidate. C is the most approved candidate and has the biggest single pairwise score (55 verus A). A has the most top rankings. Both Winning Votes and Margins (using the Schulze or equivalent algorithm) elect B, the clearly weakest candidate. Notice that electing B is another outrageous failure of Later-no-Help. Losing Votes elects A. Part of the case against electing C is that the 25 C truncators could be defecting from a sincere BC coalition (and if so, shouldn't be rewarded). Part (at least) of the case for electing C is that if the 30 BC voters are sincere (and detest A) they have a strong incentive to order-reverse and maybe C has a disincentive to run. But other than in effect just portraying the Margins or Winning Votes algorithms as in themselves standards, there is no case for electing B. Of the various proposed ways of weighing defeat strengths in Schulze, Losing Votes is the one that elects most from the tops of the ballots. Given that we are seeking to convert supporters of FPP (and to I hope a lesser extent, IRV), I think that is a marketing advantage. Chris Benham But there is no case for electing B, other than Election-Methods mailing list - see http://electorama.com/em for list info
[EM] TTR,MinMax, Losing Votes (TERW)
Here is an example of my suggested new FBC-complying method performing better than ICT (Improved Condorcet, Top, a name coined by Mike Ossipoff for a method I defined). 30: A=B 30: B 20: A 10: CA 10: DA According to the TTR (Kevin Venzke's Tied at the Top Tule), AB 70-30 and BA 60-40. A C 50-10, AD 50-10, BC 60-10, BD 60-10. Only A and B are qualified by TTR, and ICT elects the qualified candidate with highest Top ratings (we'll say these are Top-Middle-Bottom 3-slot ratings ballots, with default rating being Bottom). TR scores: B60, A50, C10, D10. So ICT elects B. The first part of my new method is the same, so only A and B are qualified. To determine the winner a different pairwise matrix is looked at to weigh defeats (while keeping the same TTR direction). So AB 70-60 and BA 60-70 (the 30 A=B ballots each give a whole vote to both A and B). A and B have no other pairwise defeats, so (weighing them by Losing Votes) A's MinMax score is 70 and B's is 60 so A wins. A is rescued from the splitting of the AB faction''s vote by C and D being on the ballot. As it does here, the new method is much more likely than ICT to elect the real Condorcet winner. Chris Benham I wrote (Tues.20 Nov 2012): I have an idea for a not-very-sinple FBC-complying method that behaves like ICT with 3 candidates, but better handles more candidates and ballots with more than 3 ratings-slots or ballots that allow full ranking of the candidates. *Voters rank from the top however many candidates they wish. Equal-top ranking and truncation must be allowed. Use the Tied-at-the-Top Rule (invented by Kevin Venzke) to discover if any candidate/s pairwise beats (according to that rule's special definition) all the others, and if so to disqualify all those that don't. http://wiki.electorama.com/wiki/Tied_at_the_top_rule Then construct a pairwise matrix that is normal except that ballots that equal-rank at the top any X and Y contribute a whole vote (in the X versus Y pairwise comparison) to each of X and Y. Ballots that equal-rank any X and Y in any below-top position contribute (in that pairwise comparison) no vote to either. The purpose of that matrix is just to determine Losing Votes scores. The directions of the defeats are determined by the Tied-at-the-Top rule (according to which X and Y can pairwise defeat each other. Elect the qualified candidate whose worse defeat (as identified by TTR and measured by Losing Votes with the above equal top-ranking rule) is the weakest.* I hope that inelegant waffle is at least clear. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Losing Votes (ERABW)
On 16 Nov 2012 07:29:52 -0800, Chris Benham wrote: It isn't a big deal if Ranked Pairs or River are used instead of Schulze. Losing Votes means that the pairwise results are weighed purely by the number of votes on the losing side. The weakest defeats are those with the most votes on the losing side, and of course conversely the strongest victories are those with the fewest votes on the losing side. Hi Chris, Just so I understand this correctly: You're saying that the pairwise contest A:3 B:1 should be weighted more strongly than C:3,000,001 D:2,999,999? Even though only 4 people care to vote in the A vs. B contest? Ted -- Ted, Yes. I'm not interested in moral arguments about this or that part of an algorithm. If you don't like it, give an example with a result you don't like. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Name of Weak Participation
Mike Ossipoff wrote: Weak Participation is such a natural consistency desideratum, it probably already has a name. Maybe it's called Mono-Add-Solo-Top. If not, that might be a good name for it. More descriptive than Weak Participation. Weak Participation: Adding a ballot shouldn't cause the defeat of the candidate whom it votes over all of the other candidates. [end of Weak Participation definition] Mono-add-Top. http://wiki.electorama.com/wiki/Mono-add-top_criterion Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] 3 or more choices - Condorcet
Ted Stern wrote (8 Nov 2012): Hi Chris, You discuss Winning Votes vs. Margins below. What do you think about using the Cardinal-Weighted Pairwise array in conjunction with the traditional Condorcet array? In other words, either WV or Margins is used to decide whether there is a defeat, but the CWP array is used to determine the defeat strength, in either Ranked Pairs or Schulze. To recap for those not familiar with the technique (due to James Green-Armytage in 2004), a ratings ballot is used: give a score of a_i to candidate i. Ranks are inferred: candidate i receives one Condorcet vote over candidate j if a_i a_j. Whenever that Condorcet vote is recorded into the standard A_ij array, you also tally the difference (a_i - a_j) into the corresponding CWP_ij location. Ted, Actually I talked more about Losing Votes than Winning Votes. I can't remember all the reasons I don't like CWP, but it is far too complicated with not enough bang for buck. I prefer Smith//Approval (ranking), or a method that Forest and I discussed a while ago. It is a bit better (and more elegant) than Smith//Approval, and nearly always gives the same winner. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] 3 or more choices - Condorcet
Robert Bristow-Johnson wrote (1 Oct 2012): my spin is similar. Ranked Pairs simply says that some elections (or runoffs) speak more loudly than others. those with higher margins are more definitive in expressing the will of the electorate than elections with small margins. of course, a margin of zero is a tie and this says *nothing* regarding the will of the electorate, since it can go either way. the reason i like margins over winning votes is that the margin, in vote count, is the product of the margin as a percent (that would be a measure of the decisiveness of the electorate) times the total number of votes (which is a measure of how important the election is). so the margin in votes is the product of salience of the race times how decisive the decision is. Say there are 3 candidates and the voters have the option to fully rank them, but instead they all just choose to vote FPP-style thus: 49: A 48: B 03: C Of course the only possible winner is A. Now say the election is held again (with the same voters and candidates), and the B voters change to BC giving: 49: A 48: BC 03: C Now to my mind this change adds strength to no candidate other than C, so the winner should either stay the same or change to C. Does anyone disagree? So how do you (Robert or whoever the cap fits) justify to the A voters (and any fair-minded person not infatuated with the Margins pairwise algorithm) that the new Margins winner is B?? The pairwise comparisons: BC 48-3, CA 51-49, AB 49-48. Ranked Pairs(Margins) gives the order BCA. I am happy with either A or C winning, but a win for C might look odd to people accustomed to FPP and/or IRV. *If* we insist on a Condorcet method that uses only information contained in the pairwise matrix (and so ignoring all positional or approval information) then *maybe* Losing Votes is the best way to weigh the pairwise results. (So the strongest pairwise results are those where the loser has the fewest votes and, put the other way, the weakest results are those where the loser gets the most votes). In the example Losing Votes elects A. Winning Votes elects C which I'm fine with, but I don't like Winning Votes for other reasons. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Two more 3-slot FBC/ABE solutions (not)
Jameson, You're not missing anything. You are right. Thanks for pointing that out. I should have thought more about those methods before suggesting them. I withdraw those suggestions. I still stand by APPMM as a good criterion. But the set can't be a component of a method algorithm that meets the FBC. Chris Benham From: Jameson Quinn jameson.qu...@gmail.com To: C.Benham cbenha...@yahoo.com.au Cc: em election-meth...@electorama.com Sent: Wednesday, 25 January 2012 5:11 AM Subject: Re: [EM] Two more 3-slot FBC/ABE solutions In fact, that would seem to be a pretty strong argument that these methods don't meet the FBC. What am I missing? 2012/1/24 Jameson Quinn jameson.qu...@gmail.com The problem with these methods is that you can't afford to vote for the marginal candidate whom only you have heard of, because that candidate will not be part of any S, and so your ballot will count against any S, even an S that you otherwise like. Jameson 2012/1/24 C.Benham cbenha...@yahoo.com.au Following on from my recent definition of the APPMM criterion/set, I'd like to propose two not bad 3-slot methods that meet the FBC.. Recall that I defined the APPMM criterion thus: *If the number of ballots on which some set S of candidates is voted strictly above all the candidates outside S is greater than the number of ballots on which any outside-S candidate is voted strictly above any member of S, then the winner must come from S.* The APPMM set is the set of candidates not disqualified by the APPMM criterion. APMM//TR: * Voters fill out 3-slot ratings ballots. Default rating is Bottom (signifying least preferred and not approved.) The other slots are Top (signifying most preferred) and Middle. From the set of candidates not disqualified by the APPMM criterion, elect the one with the most Top ratings.* APMM//CR: * Voters fill out 3-slot ratings ballots. Default rating is Bottom (signifying least preferred and not approved.) The other slots are Top (signifying most preferred) and Middle. From the set of candidates not disqualified by the APPMM criterion, elect the one with the highest Top minus Bottom ratings score.* So far I can't see that these are technically any better than my earlier suggestion of TTPBA//TR, and unlike that method they fail the Tied at the Top Pairwise Beats All criterion. But like that method they meet the Plurality and Mono-add-Plump criteria, and also have no problem with Kevin's bad MMPO example. I'm happy for APMM//CR to be also called APMM//Range. This method is more Condorcetish than APMM//TR, for example: 49: CB 27: AB 24: BA BA 73-27, BC 51-49, AC 51-49. APMM//TR elects A, while APMM//CR elects B (like TTPBA//TR). I am sure that APMM//TR has no defection incentive in the Approval Bad Example, and the other method also does in the example normally given. Of course some other points-score scheme (perhaps giving greater weight to to Top Ratings) is possible. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Approval vs. IRV (hopefully tidier re-send)
Matt Welland wrote (26 Nov 2011): Also, do folks generally see approval as better than or worse than IRV? To me Approval seems to solve the spoiler problem without introducing any unstable weirdness and it is much simpler and cheaper to do than IRV. If we are talking about the classic version of IRV known as the Alternative Vote in the UK and Optional Preferential Voting in Australia, then I see IRV on balance as being better than Approval. The version of IRV I'm referring to: *Voters strictly rank from the top however many or few candidates they wish. Until one candidate remains, one-at-a time eliminate eliminate the candidate that (among remaining candidates) is highest-ranked on the fewest ballots.* The unstable weirdness of Approval is in the strategy games among the rival factions of voters, rather than anything visible in the method's algorithm. Approval is more vulnerable to disinformation campaigns. Suppose that those with plenty of money and control of the mass media know from their polling that the likely outcome of an upcoming election is A 52%, B 48% and they much prefer B. In Approval they can sponsor and promote a third candidate C, one that the A supporters find much worse than B, and then publish false polls that give C some real chance of winning. If they can frighten/bluff some of A's supporters into approving B (as well as A) their strategy can succeed. 47: A 05: AB (sincere is AB) 41: B 07: BC Approvals: B53, A52, C7 Approval is certainly the bang for buck champion, and voters never have any incentive to vote their sincere favourites below equal-top. But to me the ballots are insufficiently expressive by comparison with the strict ranking ballots used by IRV. IRV has some Compromise incentive, but it is vastly less than in FPP. Supposing we assume that there are 3 candidates and that you the voter want (maybe for some emotional or long-term reason) to vote your sincere favourite F top even if you think (or know) that F can't win provided you don't thereby pay too high a strategic penalty, i.e. that the chance is small that by doing that you will lose some (from your perspective positive) effect you might otherwise have had on the result. In FPP, to be persuaded to Compromise (i.e.vote for your compromise might win candidate C instead of your sincere favourite F) you only have to be convinced that F won't be one of the top two first-preference place getters. In IRV if you are convinced of that you have no compelling reason to compromise because you can expect F to be eliminated and your vote transferred to C. No, to have a good reason to compromise you must be convinced that F *will* be one of the top 2 (thanks to your vote) displacing C, but will nonetheless lose when C would have won if you'd top-voted C. In my opinion IRV is one of the reasonable algorithms to use with ranked ballots, and the best for those who prefer things like Later-no-Harm and Invulnerability to Burial to either the Condorcet or FBC criteria. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] An ABE solution
Forest, In reference to your new Condorcet method suggestion (pasted at the bottom), which elects an uncovered candidate and if there is none one-at-time disqualifies the Range loser until a remaining candidate X covers all the other remaining candidates and then elects X, you wrote: Indeed, the three slot case does appear to satisfy the FBC... No. Here is my example, based on that Kevin Venke proof you didn't like. Say sincere is 3: BA 3: A=C 3: B=C 2: AC 2: BA 2: CB 1: C Range (0,1,2) scores: C19, B17, A12. CB 8-5, BA 10-5, AC 7-6. C wins. Now we focus on the 3 BA preferrers. Suppose (believing the method meets the FBC) they vote B=A. 3: B=A (sincere is BA) 3: A=C 3: B=C 2: AC 2: BA 2: CB 1: C Range (0,1,2) scores: C19, B17, A15. CB 8-5, BA 7-5, AC 7-6. C still wins. Now suppose they instead rate their sincere favourite Middle: 3: AB (sincere is BA) 3: A=C 3: B=C 2: AC 2: BA 2: CB 1: C Range (0,1,2) scores: C19, A15, B12. AB 8-7, AC 7-6, CB 8-5 Now those 3 voters get a result they prefer, the election of their compromise candidate A. Since it is clear they couldn't have got a result for themselves as good or better by voting BA or BC or B this is a failure of the FBC. Chris Benham From: fsimm...@pcc.edu fsimm...@pcc.edu Sent: Wednesday, 23 November 2011 9:01 AM Subject: Re: An ABE solution voters to avoid the middle slot. Then the method reduces to Approval, which does satisfy the FBC. The FBC doesn't stipulate that all the voters use optimal strategy, so that isn't relavent. http://wiki.electorama.com/wiki/FBC http://nodesiege.tripod.com/elections/#critfbc Chris Benham Forest Simmons wrote (17 Nov 2011): Here’s my current favorite deterministic proposal: Ballots are Range Style, say three slot for simplicity. When the ballots are collected, the pairwise win/loss/tie relations are determined among the candidates. The covering relations are also determined. Candidate X covers candidate Y if X beats Y as well as every candidate that Y beats. In other words row X of the win/loss/tie matrix dominates row Y. Then starting with the candidates with the lowest Range scores, they are disqualified one by one until one of the remaining candidates X covers any other candidates that might remain. Elect X. You are right that although the method is defined for any number of slots, I suggested three slots as most practical. So my example of two slots was only to disprove the statement the assertion that the method cannot be FBC compliant, since it is obviously compliant in that case. Furthermore something must be wrong with the quoted proof (of the incompatibility of the FBC and the CC) because the winner of the two slot case can be found entirely on the basis of the pairwise matrix. The other escape hatch is to say that two slots are not enough to satisfy anything but the voted ballots version of the Condorcet Criterion. But this applies equally well to the three slot case. Either way the cited therorem is not good enough to rule out compliance with the FBC by this new method. Indeed, the three slot case does appear to satisfy the FBC as well. It is an open question. I did not assert that it does. But I did say that IF it is strategically equivalent to Approval (as Range is, for example) then for practical purposes it satisfies the FBC. Perhaps not the letter of the law, but the spirit of the law. Indeed, in a non-stratetgical environment nobody worries about the FBC, i.e. only strategic voters will betray their favorite. If optimal strategy is approval strategy, and approval strategy requires you to top rate your favorite, then why would you do otherwise? Forest - Original Message - From: Chris Benham Forest, When the range ballots have only two slots, the method is simply Approval, which does satisfy the FBC. When you introduced the method you suggested that 3-slot ballots be used for simplicity. I thought you might be open to say 4-6 slots, but a complicated algorithm on 2-slot ballots that is equivalent to Approval ?? Now consider the case of range ballots with three slots: and suppose that optimal strategy requires the Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] An ABE solution
Jameson, Your range scores are a little bit wrong,.. I've re-checked them and I don't see how. I gave each candidate 2 points for a top-rating, 1 for a middle-rating and zero for a bottom rating (or truncation). So in the initial sincere scenario for example C has 9 top-ratings and 1 middle-rating to make a score of 19, B has 8 top-ratings and 1 middle-rating to make a score of 17, and A has 5 top-ratings and 2 middle-ratings to make a score of 12. Chris Benham From: Jameson Quinn jameson.qu...@gmail.com Sent: Friday, 25 November 2011 5:39 AM Subject: Re: An ABE solution Chris: Your range scores are a little bit wrong, so you have to add half a B vote for the example to work (or double all factions and add one B vote if you discriminate against fractional people), but yes, this is at heart a valid example where the method fails FBC. Note that in my tendentious terminology this is only a defensive failure, that is, it starts from a position of a sincere condorcet cycle, which I believe will be rare enough in real elections to be discountable. In particular, this failure does not result in a stable two-party-lesser-evil-strategy self-reinforcing equilibrium. Jameson 2011/11/24 Chris Benham cbenha...@yahoo.com.au Forest, In reference to your new Condorcet method suggestion (pasted at the bottom), which elects an uncovered candidate and if there is none one-at-time disqualifies the Range loser until a remaining candidate X covers all the other remaining candidates and then elects X, you wrote: Indeed, the three slot case does appear to satisfy the FBC... No. Here is my example, based on that Kevin Venke proof you didn't like. Say sincere is 3: BA 3: A=C 3: B=C 2: AC 2: BA 2: CB 1: C Range (0,1,2) scores: C19, B17, A12. CB 8-5, BA 10-5, AC 7-6. C wins. Now we focus on the 3 BA preferrers. Suppose (believing the method meets the FBC) they vote B=A. 3: B=A (sincere is BA) 3: A=C 3: B=C 2: AC 2: BA 2: CB 1: C Range (0,1,2) scores: C19, B17, A15. CB 8-5, BA 7-5, AC 7-6. C still wins. Now suppose they instead rate their sincere favourite Middle: 3: AB (sincere is BA) 3: A=C 3: B=C 2: AC 2: BA 2: CB 1: C Range (0,1,2) scores: C19, A15, B12. AB 8-7, AC 7-6, CB 8-5 Now those 3 voters get a result they prefer, the election of their compromise candidate A. Since it is clear they couldn't have got a result for themselves as good or better by voting BA or B=A or B or BC or B=C this is a failure of the FBC. Chris Benham From: fsimm...@pcc.edu fsimm...@pcc.edu Sent: Wednesday, 23 November 2011 9:01 AM Subject: Re: An ABE solution You are right that although the method is defined for any number of slots, I suggested three slots as most practical. So my example of two slots was only to disprove the statement the assertion that the method cannot be FBC compliant, since it is obviously compliant in that case. Furthermore something must be wrong with the quoted proof (of the incompatibility of the FBC and the CC) because the winner of the two slot case can be found entirely on the basis of the pairwise matrix. The other escape hatch is to say that two slots are not enough to satisfy anything but the voted ballots version of the Condorcet Criterion. But this applies equally well to the three slot case. Either way the cited therorem is not good enough to rule out compliance with the FBC by this new method. Indeed, the three slot case does appear to satisfy the FBC as well. It is an open question. I did not assert that it does. But I did say that IF it is strategically equivalent to Approval (as Range is, for example) then for practical purposes it satisfies the FBC. Perhaps not the letter of the law, but the spirit of the law. Indeed, in a non-stratetgical environment nobody worries about the FBC, i.e. only strategic voters will betray their favorite. If optimal strategy is approval strategy, and approval strategy requires you to top rate your favorite, then why would you do otherwise? Forest - Original Message - From: Chris Benham Forest, When the range ballots have only two slots, the method is simply Approval, which does satisfy the FBC. When you introduced the method you suggested that 3-slot ballots be used for simplicity. I thought you might be open to say 4-6 slots, but a complicated algorithm on 2-slot ballots that is equivalent to Approval ?? Now consider the case of range ballots with three slots: and suppose that optimal strategy requires the voters to avoid the middle slot. Then the method reduces to Approval, which does satisfy the FBC. The FBC doesn't stipulate that all the voters use optimal strategy, so that isn't relavent. http://wiki.electorama.com/wiki/FBC http://nodesiege.tripod.com/elections/#critfbc Chris Benham Forest Simmons wrote (17 Nov 2011): Here’s my current favorite
Re: [EM] An ABE solution
Forest,
When the range ballots have only two slots, the method is simply Approval,
which does satisfy the
FBC.
When you introduced the method you suggested that 3-slot ballots be used for
simplicity.
I thought you might be open to say 4-6 slots, but a complicated algorithm on
2-slot ballots
that is equivalent to Approval ??
Now consider the case of range ballots with three slots: and suppose that
optimal strategy requires the
voters to avoid the middle slot. Then the method reduces to Approval, which
does satisfy the FBC.
The FBC doesn't stipulate that all the voters use optimal strategy, so that
isn't relavent.
http://wiki.electorama.com/wiki/FBC
http://nodesiege.tripod.com/elections/#critfbc
Chris Benham
From: fsimm...@pcc.edu fsimm...@pcc.edu
To: C.Benham cbenha...@yahoo.com.au
Cc: em election-meth...@electorama.com; MIKE OSSIPOFF nkk...@hotmail.com
Sent: Tuesday, 22 November 2011 11:11 AM
Subject: Re: An ABE solution
From: C.Benham
Forest Simmons, responding to questions from Mike Ossipff, wrote
(19 Nov
2011):
4. How does it do by FBC? And by the criteria that bother some
people here about MMPO (Kevin's MMPO bad-example) and MDDTR
(Mono-Add-Plump)?
I think it satisfies the FBC.
Forest's definition of the method being asked about:
Here’s my current favorite deterministic proposal: Ballots are
Range
Style, say three slot for simplicity.
When the ballots are collected, the pairwise win/loss/tie
relations are
determined among the candidates.
The covering relations are also determined. Candidate X covers
candidate Y if X
beats Y as well as every candidate that Y beats. In other
words row X
of the
win/loss/tie matrix dominates row Y.
Then starting with the candidates with the lowest Range
scores, they are
disqualified one by one until one of the remaining candidates
X covers
any other
candidates that might remain. Elect X.
Forest,
Doesn't this method meet the Condorcet criterion? Compliance
with
Condorcet is incompatible with FBC, so
why do you think it satisfies FBC?
When the range ballots have only two slots, the method is simply Approval,
which does satisfy the
FBC. Does Approval satisfy the Condorcet Criterion? I would say no, but it
does satisfy the votes only
Condorcet Criterion. which means that the Approval winner X pairwise beats
every other candidate Y
according to the ballots, i.e. X is rated above Y on more ballots than Y is
rated above X.
Now consider the case of range ballots with three slots: and suppose that
optimal strategy requires the
voters to avoid the middle slot. Then the method reduces to Approval, which
does satisfy the FBC.
http://lists.electorama.com/pipermail/election-methods-
electorama.com/2005-June/016410.html
Hello,
This is an attempt to demonstrate that Condorcet and FBC are
incompatible. I modified Woodall's proof that Condorcet and
LNHarm are incompatible.
(Douglas R. Woodall, Monotonicity of single-seat preferential
election rules,
Discrete Applied Mathematics 77 (1997), pages 86 and 87.)
I've suggested before that in order to satisfy FBC, it must be
the case
that increasing the votes for A over B in the pairwise matrix
can never
increase the probability that the winner comes from {a,b};
that is, it
must
not move the win from some other candidate C to A. This is
necessary
because
if sometimes it were possible to move the win from C to A by
increasing v[a,b], the voter with the preference order BAC
would have incentive to
reverse B and A in his ranking (and equal ranking would be
inadequate).
I won't presently try to argue that this requirement can't be
avoided
somehow.
I'm sure it can't be avoided when the method's result is
determined solely
from the pairwise matrix.
Note that in our method the Cardinal Ratings order (i.e. Range Order) is needed
in addition to the
pairwise matrix; the covering information comes from the pairwise matrix, but
candidates are dropped
from the bottom of the range order.
In the two slot case can the approval order be determined from the pairwise
matrix? If so, then this is a
counterexample to the last quoted sentence above in the attempted proof of the
incompatibility of the CC
and the FBC.
Forest
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] IRV variants
Forest, the IRV- Condorcet you describe here is a simpler solution, as long as you allow equal rankings, and count them as whole (as opposed to fractional): I am strongly opposed to allowing equal ranking (except for truncation) in IRV or IRV-like Condorcet methods. As I've explained more than once on EM, that just makes Push-over strategising much easier. And in this respect the whole vote version is much worse than the fractional version. If you are confident that your favourite will make the final runoff and that your favourite will have a pairwise win versus some turkey with you being merely neutral (not supporting the turkey as you'd have to do in regular IRV) then you should vote the turkey equal-top with your favourite. You are still giving a whole vote to help your favourite make the top 2, so on the whole the strategy is much less risky and easier to carry out than with regular IRV and to a lesser extent the Fractional version. Chris From: fsimm...@pcc.edu fsimm...@pcc.edu To: C.Benham cbenha...@yahoo.com.au Cc: em election-meth...@electorama.com Sent: Thursday, 10 November 2011 5:54 AM Subject: Re: IRV variants I don't get it. (I am confused by your explanation of the algorithm). How do you think this is better than your latest version of Enhanced DMC? It takes care of the chicken problem. But forget my confusing process; the IRV- Condorcet you describe here is a simpler solution, as long as you allow equal rankings, and count them as whole (as opposed to fractional): I think a good method is the IRV-Condorcet hybrid that differs from IRV only by before any and each elimination checks for an uneliminated candidate X that pairwise beats all the other uneliminated candidates and elects the first such X to appear. Yes this is simpler. That of course gains Condorcet, and it keeps IRV's Mutual Dominant Third Burial Resistance property. So if a candidate X pairwise beats all the other candidates and is ranked above all the other candidates on more than a third of the ballots then (as with IRV) X must win and a rival candidate Y's supporters can't get Y elected (assuming they can somehow change their ballots) by Burying X. Does your method share that property? 49 C 27 AB 24 B Candidate A starts out as underdog, survives B, and is beaten by C, so C wins. From what I think I do understand of your algorithm description, doesn't candidate B start out as underdog? Yes, I was in too much of a hurry when I wrote that. Also contrary to my hopes the method turned out to be non-monotonic, because the IRV elimination order can eliminate a candidate earlier as a result of more first place support. Only elimination orders without this defect can be used as a basis for a monotone method. Forest Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Enhanced DMC (correction)
I got the Woodall monotonicity criterion garbled. Instead of
mono-sub-delete and then
mono-raise-delete, in both instances I meant *mono-sub-plump*. (I've made
the corrections
in the text below.)
It means that candidate x shouldn't be harmed (i.e. have his probability of
election reduced)
by swapping some ballots that don't have x top-ranked for some that rank x
alone in top place
and ignore (or vote equal-bottom) all the other candidates.
In the context of a universe of ballots that allow only strict ranking from
the top, with truncation
(but no other equal-ranking) allowed, Woodall defined it:
snip
A candidate x should not be harmed if:
(
are replaced by ballots that have
choice;
snip
http://f1.grp.yahoofs.com/v1/4CSOTg18Jla8JeZD7lGf-L15LhewtDexi1BvIN9JQ79d6fDKQfZlI5ygNNqdMM_8b3XPbatc01XxYUjo1LgxMq9WirJdubA/wood1996.pdf
mono-sub-plump) some ballots that do not have x topx top with no second
Also I referred to Push-over strategy. That refers to the strategy
of raising some weak candidate to enable
some other candidate to win (or to have a better chance of winning).
It was coined with methods like Top-Two Runoff and IRV in mind. Perhaps
Push-over *like* strategy was
more apt for the methods I referred to.
Chris Benham
---
I like this. Regarding how approval is inferred, I'm also happy with Forest's
idea of using Range
(aka Score) type ballots (on which voters give their most preferred candidates
the highest numerical
scores) and interpreting any score above zero as approval and breaking approval
ties as any score
above 1 etc. Or any other sort of multi-slot ratings ballot where all except
the bottom-most slot is
interpreted as approval.
Another idea is to enter above-bottom equal-ranking between any 2 candidates in
the pairwise matrix
as a whole vote for both candidates, and then take each candidate X's highest
single pairwise score
as X's approval score.
Here are a couple of examples to demonstrate how this method varies from some
other Condorcet
methods.
48: A
01: AD
24: BD
27: CBD
D is the most approved candidate and in the Smith set, and so Smith//Approval
elects D.
Forest's Enhanced DMC or Covering DMC (and your suggested SARR
implementation)
elects B.
B covers D and to me looks like a better winner. This method has a weaker
truncation incentive
than Smith//Approval.
25: AB
27: BC
26: CA
22: C
Approvals: C75, B52, A51. AB 51-49, BC 52-48, CA 75-25
Plain DMC and using MinMax or one of the algorithms that is equivalent to it
when there are three
candidates (such as Schulze and Ranked Pairs and River) and weighing defeats
either by Winning
Votes or Margins all elect B.
If 5 of the 22 C voters change to A those methods all elect C (a failure of
Woodall's mono-sub-plump
criterion).
25: AB
27: BC
26: CA
17: C
05: A (was C)
Approvals: C70, A56, B52. AB 56-49, BC 52-48, CA 70-30.
In both cases our favoured method (like Smith//Approval) elects C, the
positionally dominant candidate. It
seems those other methods are more vulnerable to Push-over strategy.
(To be fair, Woodall has demonstrated that no Condorcet method can meet
mono-sub-plump)
Chris Benham
From: Ted Stern araucaria.arauc...@gmail.com
To: election-methods@lists.electorama.com
Cc: Forest Simmons fsimm...@pcc.edu; Chris Benham cbenha...@yahoo.com.au
Sent: Wednesday, 5 October 2011 8:35 AM
Subject: Re: [EM] Enhanced DMC
After some private email exchanges with Forest and Chris, I'm
proposing a simple way of implementing Enhanced DMC, plus a new name,
Strong Approval Round Robin Voting (SARR Voting).
Ballot:
Ranked Voting, all explicitly ranked candidates considered approved.
Equal ranking allowed. I'm basing this on recommendation from Chris
Benham. I'm open to alternatives, but it seems to be the easiest way
to do it for now, and the most resistant to burying strategies.
Tallying:
Form the pairwise matrix, using the standard Condorcet procedure. In
the diagonal entries, save total Approval votes.
For N candidates, the list of candidates in order from highest to
lowest approval is
X_0, X_1, ..., X_k, X_{k+1}, ..., X_{N-1}
Initialize the Strong set to the empty set
Initialize the Weak set to the empty set.
For k = 0 to N-1,
If X_k is already in the Weak set, continue iterating. (X_k is
defeated by a higher approved candidate. This is called being
strongly defeated.)
If X_k loses to a member of the Weak set, continue iterating. (X_k
may defeat all higher approved candidates, but is weakly defeated
by at least one of them.)
If we're still here in the loop, X_k defeats all candidates in the
Strong Set and all candidates in the Weak set. (X_k covers all
previously added members of the Strong set.)
Add X_k to the Strong set and add all of X_k's defeats to the Weak
set.
Set the provisional winner to X_k.
The last provisional winner (the last candidate added to the Strong
Re: [EM] Enhanced DMC
I like this. Regarding how approval is inferred, I'm also happy with Forest's
idea of using Range
(aka Score) type ballots (on which voters give their most preferred candidates
the highest numerical
scores) and interpreting any score above zero as approval and breaking approval
ties as any score
above 1 etc. Or any other sort of multi-slot ratings ballot where all except
the bottom-most slot is
interpreted as approval.
Another idea is to enter above-bottom equal-ranking between any 2 candidates in
the pairwise matrix
as a whole vote for both candidates, and then take each candidate X's highest
single pairwise score
as X's approval score.
Here are a couple of examples to demonstrate how this method varies from some
other Condorcet
methods.
48: A
01: AD
24: BD
27: CBD
D is the most approved candidate and in the Smith set, and so Smith//Approval
elects D.
Forest's Enhanced DMC or Covering DMC (and your suggested SARR
implementation)
elects B.
B covers D and to me looks like a better winner. This method has a weaker
truncation incentive
than Smith//Approval.
25: AB
27: BC
26: CA
22: C
Approvals: C75, B52, A51. AB 51-49, BC 52-48, CA 75-25
Plain DMC and using MinMax or one of the algorithms that is equivalent to it
when there are three
candidates (such as Schulze and Ranked Pairs and River) and weighing defeats
either by Winning
Votes or Margins all elect B.
If 5 of the 22 C voters change to A those methods all elect C (a failure of
Woodall's mono-sub-delete
criterion).
25: AB
27: BC
26: CA
17: C
05: A (was C)
Approvals: C70, A56, B52. AB 56-49, BC 52-48, CA 70-30.
In both cases our favoured method (like Smith//Approval) elects C, the
positionally dominant candidate. It
seems those other methods are more vulnerable to Push-over strategy.
(To be fair, Woodall has demonstrated that no Condorcet method can meet
mono-raise-delete.)
Chris Benham
From: Ted Stern araucaria.arauc...@gmail.com
To: election-methods@lists.electorama.com
Cc: Forest Simmons fsimm...@pcc.edu; Chris Benham cbenha...@yahoo.com.au
Sent: Wednesday, 5 October 2011 8:35 AM
Subject: Re: [EM] Enhanced DMC
After some private email exchanges with Forest and Chris, I'm
proposing a simple way of implementing Enhanced DMC, plus a new name,
Strong Approval Round Robin Voting (SARR Voting).
Ballot:
Ranked Voting, all explicitly ranked candidates considered approved.
Equal ranking allowed. I'm basing this on recommendation from Chris
Benham. I'm open to alternatives, but it seems to be the easiest way
to do it for now, and the most resistant to burying strategies.
Tallying:
Form the pairwise matrix, using the standard Condorcet procedure. In
the diagonal entries, save total Approval votes.
For N candidates, the list of candidates in order from highest to
lowest approval is
X_0, X_1, ..., X_k, X_{k+1}, ..., X_{N-1}
Initialize the Strong set to the empty set
Initialize the Weak set to the empty set.
For k = 0 to N-1,
If X_k is already in the Weak set, continue iterating. (X_k is
defeated by a higher approved candidate. This is called being
strongly defeated.)
If X_k loses to a member of the Weak set, continue iterating. (X_k
may defeat all higher approved candidates, but is weakly defeated
by at least one of them.)
If we're still here in the loop, X_k defeats all candidates in the
Strong Set and all candidates in the Weak set. (X_k covers all
previously added members of the Strong set.)
Add X_k to the Strong set and add all of X_k's defeats to the Weak
set.
Set the provisional winner to X_k.
The last provisional winner (the last candidate added to the Strong
set) is the winner of the election.
Note:
The first member of the Strong Set will be X_0.
It is easiest to do this by hand if you first permute the pairwise
array so that it follows the same X_0, ..., X_{N-1} ordering.
As an example election, consider the one on this page:
http://wiki.electorama.com/wiki/Marginal_Ranked_Approval_Voting
Iterating through E, A, C, B, D, we find
E: Strong and Weak Sets are empty, so E has no losses to either.
Strong set = {E}; Weak set = {C, D}
Provisional winner set to E.
A: A defeats Strong set {E} and Weak set {C, D}.
= Strong set = {E, A}; Weak set = {C, D}
Provisional winner set to A.
C: in Weak set, not added to Strong set.
B: Defeats A, but is defeated by D from Weak set (and is therefore
weakly defeated by A).
D: in Weak set, not added to Strong set.
A is the last candidate added to the Strong set, so A wins.
Ted
--
araucaria dot araucana at gmail dot com
On 26 Sep 2011 11:44:13 -0700, Chris Benham wrote:
Forest,
I think in general that if the approval scores are at all valid I
would go for the enhanced DMC winner over any of the chain building
methods we have considered. I think other considerations over-ride
Re: [EM] Enhanced DMC
Forest,
I think in general that if the approval scores are at all valid I would go for
the enhanced DMC winner over
any of the chain building methods we have considered. I think other
considerations over-ride the
importance of being uncovered.
I agree. I think the chain building method in comparison seems a bit arbitrary
and less philosophically justified.
Also the method has a fairly straight-forward description that doesn't need to
mention Smith set or the Condorcet winner.
So of these similar methods (that include Smith//Approval and all elect the
same winner if the Smith set contains 3 members or 1 member),
I think this is my favourite.
Maybe it could use a new name? :)
Chris
From: fsimm...@pcc.edu fsimm...@pcc.edu
To: C.Benham cbenha...@yahoo.com.au
Cc: election-methods-electorama@electorama.com
Sent: Monday, 12 September 2011 8:50 AM
Subject: Re: Enhanced DMC
Very good Chris.
I tried to build a believable profile of ballots that would yield the approval
order and defeats of this
example without success, but I am sure that it is not impossible.
I think in general that if the approval scores are at all valid I would go for
the enhanced DMC winner over
any of the chain building methods we have considered. I think other
considerations over-ride the
importance of being uncovered.
- Original Message -
From: C.Benham
Date: Sunday, September 11, 2011 10:08 am
Subject: Enhanced DMC
To: election-methods-electorama@electorama.com
Cc: Forest W Simmons
Forest Simmons wrote (15 Aug 2011):
Here's a possible scenario:
Suppose that approval order is alphabetical from most approval
to least A, B, C, D.
Suppose further that pairwise defeats are as follows:
CADBA together with BCD .
Then the set P = {A, B} is the set of candidates neither of
which is pairwise
beaten by anybody with greater approval.
Since the approval winner A is not covered by B, it is not
covered by any
member of P, so the enhanced version of DMC elects A.
But A is covered by C so it cannot be elected by any of the
chain building
methods that elect only from the uncovered set.
Forest,
Is the Approval Chain-Building method the same as simply
electing the
most approved uncovered candidate?
I surmise that the set of candidates not pairwise beaten by a
more
approved candidate (your set P, what I've
been referring to as the Definite Majority set) and the
Uncovered set
don't necessarily overlap.
If forced to choose between electing from the Uncovered set and
electing
from the DM set, I tend towards
the latter.
Since Smith//Approval always elects from the DM set, and your
suggested
enhanced DMC (elect the most
approved member of the DM set that isn't covered by another
member)
doesn't necessarily elect from the Uncovered set;
there doesn't seem to be any obvious philosophical case that
enhanced
DMC is better than Smith//Approval.
(Also I would say that an election where those two methods
produce
different winners would be fantastically unlikely.)
A lot of Condorcet methods are promoted as being able to give
the
winner just from the information contained in the
gross pairwise matrix. I think that the same is true of these
methods
if we take a candidate X's highest gross pairwise
score as X's approval score. Can you see any problem with that?
Chris Benham
- Original Message -
From:
Date: Friday, August 12, 2011 3:12 pm
Subject: Enhanced DMC
To: election-methods at lists.electorama.com,
From: C.Benham
To: election-methods-electorama.com at electorama.com
Subject: [EM] Enhanced DMC
Forest,
The D in DMC used to stand for *Definite*.
Yeah, that's what we finally settled on.
I like (and I think I'm happy to endorse) this Condorcet method
idea, and consider it to be clearly better than regular DMC
Could this method give a different winner from the (Approval
Chain Building ?) method you mentioned in the C//A thread
(on 11
June 2011)?
Yes, I'll give an example when I get more time. But for all
practical
purposes they both pick the highest approval Smith candidate.
Here's a possible scenario:
Suppose that approval order is alphabetical from most approval
to least
A, B, C, D.
Suppose further that pairwise defeats are as follows:
CADBA together with BCD .
Then the set P = {A, B} is the set of candidates neither of
which is
pairwise
beaten by anybody with greater approval.
Since the approval winner A is not covered by B, it is not
covered by any
member of P, so the enhanced version of DMC elects A.
But A is covered by C so it cannot be elected by any of the
chain building
methods that elect only from the uncovered set.
Forest Simmons wrote (12 June 2011):
I think the following complete description is simpler than anything
possible for ranked pairs:
1. Next to each candidate
[EM] Looking for the name of a Bucklin variant
Michael, The method you describe was invented by Douglas Woodall and is called Quota-Limited Trickle Down. I don't think that anyone now claims that it is a very good single-winner method, but maybe you can base an ok multi-winner method on it that meets Droop Proportionality. Woodall had it meeting Majority for Solid Coalitions, his Plurality criterion, mono-raise, mono-remove-bottom, mono-raise-delete, mono-sub-plump, mono-add-plump, mono-append and Later-no-Help. And failing Clone-Winner, Clone-Loser, Condorcet, mono-add-top, mono-sub-top and Later-no-Harm. Chris Benham Michael Rouse wrote (25 Aug 2010): I was wondering if someone on the Election Methods list could give me the name (or better yet, a link to more information) on a particular variation of the Bucklin method. In Bucklin, you check first place votes to see if a candidate has a majority. If not, you add second place votes, then third place votes and so on, until at least one candidate has a majority. In the variation I'm thinking of, you look at first place votes. If one candidate has a majority, then he or she is the winner; otherwise, you start adding second place votes *one at a time* (rather than all at once), until you have majority candidate. If no candidate has a majority, you start adding third place votes one at a time, and so on. In other words, you find the candidate who needs the fewest added votes at a particular rank to be a majority winner. If candidate A needs only 2 second-place votes to have a majority and candidate B needs 100, it wouldn't matter that candidate A has only 3 second place votes and B has 1000. I know this has to have a name (or at least someone has looked at it and given a nice description of its properties), and I'm interested in seeing how it would apply to multi-winner elections without reinventing the wheel. Thanks! Michael Rouse Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Irrelevant Ballots Independent Fallback Approval (IBIFA)
Irrelevant Ballots Independent Fallback Approval (IBIFA) is the name I've settled on for the method I proposed in a May 2010 EM post titled Bucklin-like method meeting Favorite Betrayal and Irrelevant Ballots. http://lists.electorama.com/pipermail/election-methods-electorama.com/2010-May/026479.html In that post I wrote that it uses multi-slot ratings ballots, and defined the 4-slot version: *Voters fill out 4-slot ratings ballots, rating each candidate as either Top, Middle1, Middle2 or Bottom. Default rating is Bottom, signifying least preferred and unapproved. Any rating above Bottom is interpreted as Approval. If any candidate/s X has a Top-Ratings score that is higher than any other candidate's approval score on ballots that don't top-rate X, elect the X with the highest TR score. Otherwise, if any candidate/s X has a Top+Middle1 score that is higher than any other candidate's approval score on ballots that don't give X a Top or Middle1 rating, elect the X with the highest Top+Middle1 score. Otherwise, elect the candidate with the highest Approval score.*(Obviously other slot names are possible, such as 3 2 1 0 or A B C D or Top, High Middle, Low Middle, Bottom.) The 3-slot version: *Voters fill out 3-slot ratings ballots, rating each candidate as either Top, Middle or Bottom. Default rating is Bottom, signifying least preferred and unapproved. Any rating above Bottom is interpreted as Approval. If any candidate/s X has a Top-Ratings score that is higher than any other candidate's approval score on ballots that don't top-rate X, elect the X with the highest TR score. Otherwise, elect the candidate with the highest Approval score.* It can also be adapted for use with ranked ballots: *Voters rank the candidates, beginning with those they most prefer. Equal-ranking and truncation are allowed. Ranking above at least one other candidate is interpreted as Approval. The ballots are interpreted as multi-slot ratings ballots thus: An approved candidate ranked below zero other candidates is interpreted as Top-Rated. An approved candidate ranked below one other candidate is interpreted as being in the second-highest ratings slot. An approved candidate ranked below two other candidates is interpreted as being in the third-highest ratings slot (even if this means the second-highest ratings slot is left empty). An approved candidate ranked below three other candidates is interpreted as being in the fourth-highest ratings slot (even if this means that a higher ratings slot is left empty). And so on. Say we label these ratings slot from the top A B C D etc. A candidate X's A score is the number of ballots on which it is A rated. A candidate X's A+B score is the number of ballots on which it is rated A or B. A candidate X's A+B+C score is the number of ballots on which it is rated A or B or C. And so on. If any candidate X has an A score that is greater than any other candidate's approval score on ballots that don't A-rate X, then elect the X with the greatest A score. Otherwise, if any candidate X has an A+B score that is greater than any other candidate's approval score on ballots that don't A-rate of B-rate X, then elect the X with the greatest A+B score. And so on as in the versions that use a fixed number of ratings slots, if necessary electing the most approved candidate.* This is analogous with ER-Bucklin(whole) on ranked ballots: http://wiki.electorama.com/wiki/ER-Bucklin Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Condorcet question - why not bullet vote?
Peter, If I just bullet vote in a Condorcet election, then I increase the chances of my candidate being elected. Bullet voting in an election using a method that complies with the Condorcet criterion does I suppose somewhat increase the chance of your candidate being the Condorcet winner. But all Condorcet methods fail Later-no-Help, and in some this effect is sufficiently strong for the method to have a random fill incentive. That means that if you know nothing about how other voters will vote you are probabilistically better off by strictly ranking all your least preferred candidates. 46: AB 44: B 10: C Here A is the CW, but if the 44B voters change to BC then Schulze(Winning Votes) elects B. Schulze (WV) also has a zero-info. equal-rank at the top incentive. So say you know nothing about how other voters will vote and you have a big gap in your sincere ratings of the candidates, then your best probabilistic strategy is to rank all the candidates in your preferred group (those above the big gap in your ratings) equal-top and to strictly rank (randomly if necessarily) all the candidates below the gap. Your question seems to come with assumption that the voter doesn't care much who wins if her favourite doesn't. Q: In this case why should any voter not bullet-vote? The voter might be mainly interested in preventing her least preferred candidate from winning. Bullet voting is then a worse strategy than ranking that hated candidate strictly bottom. Another Condorcet method is Smith//Approval(ranking). That interprets ranking versus truncation as approval and elects the member of the Smith set (the smallest subset S of candidates that pairwise beat any/all non-S candidates) that has the highest approval score. (Some advocate the even simpler Condorcet//Approval(ranking) that simply elects the most approved candidate if there is no single Condorcet winner.) In the example above the effect of the 44B voters changing to BC is with those methods to make C the new winner. Those methods do have a truncation incentive, so then many voters who are mainly interested in getting their strict favourites elected will and should bullet vote. What is wrong with that? Chris Benham Dear all, dear Markus Schulze,I got a second question from one of our members (actually the same guy which asked for the first time): If I just bullet vote in a Condorcet election, then I increase the chances of my candidate being elected. If I have a second or third option, the chances of my prefered candidate to win is lowered. Q: In this case why should any voter not bullet-vote? I have some clue on how to answer, but not enough for an exhaustive answer.My argument starts: If I vote for a candidate who has 50% of the votes, then it does not matter if there is a second or third choice. If my prefered candidate A gets 50% of the votes, then it makes sense to support a second choice candidate B. However if the supporters of B only bullet vote, then maybe B's supporters get an advantage over A? ... at this point I realize, that I don't know enough about Condorcet and/or Schulze to answer the question.Why is it not rational to bullet vote in a Condorcet election if you are allowed not to rank some candidates? I guess you have discussed this question a zillion of times, so please forgive my ignorance.Maybe you could help me out with this one. Peter Election-Methods mailing list - see http://electorama.com/em for list info
[EM] methods based on cycle proof conditions
I. BDR or Bucklin Done Right: Use 4 levels, say, zero through three. First eliminate all candidates defeated pairwise with a defeat ratio of 3 to 1. Then collapse the top two levels, and eliminate all candidates that suffer a defeat ratio of 2 to 1. If any candidates are left, among these elect the one with the greatest number of positive ratings. snip This seems to be even more Approvalish than normal Bucklin. 65: A3, B2 35: B3, A0 (I assume that zero indicates least preferred) Forest's BDR method elects A, failing Majority Favourite. In response to the above, Abd Lomax-Smith wrote (3 June 2010): snip Now, who would use BDR with only two candidates? It's like using Range with only two candidates. Why would you care about majority favorite if you decide to use raw range. I wonder why the A faction even bothered to vote with that pattern of utilities (ratings). That's what is completely unrealistic about this kind of analysis. snip I was content to simply prove that the method simply fails Majority Favourite, but to appease Abd here is a similar example with three candidates: 60: A3, B1, C0 35: B3, A0, C1 05: C3, A2, C0 A is the big majority favourite and the big voted raw range winner, and yet B wins. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] methods based on cycle proof conditions
Forest Simmons wrote (1 June 2010): snip I. BDR or Bucklin Done Right: Use 4 levels, say, zero through three. First eliminate all candidates defeated pairwise with a defeat ratio of 3 to 1. Then collapse the top two levels, and eliminate all candidates that suffer a defeat ratio of 2 to 1. If any candidates are left, among these elect the one with the greatest number of positive ratings. snip This seems to be even more Approvalish than normal Bucklin. 65: A3, B2 35: B3, A0 (I assume that zero indicates least preferred) Forest's BDR method elects A, failing Majority Favourite. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Tanking advantage of cycle proof conditions
Forest Simmons wrote (29 May 2010): Here's a four slot method that takes advantage of the impossibility of beat cycles under certain conditions:. Use range style ballots with four levels: 0, 1, 2, and 3. (1) First eliminate all candidates that are pairwise defeated by a ratio greater than 3/1. (2) Then eliminate all of the candidates that are pairwise defeated by a ratio greater than 2/1 based on only those comparisons that involve an extreme rating, i.e. 3 beats a 0, 1, or 2, while 1, 2, or 3 beats a 0, but don't count a 2 as beating a 1, since neither 1 not 2 is an extreme rating on our four slot ballot. (3) Finally, eliminate all of the candidates that are pairwise defeated by any ratio greater than 1/1 on the basis of comparisons that involve a rating difference of at least two, i.e. 3 vs. 0 or 1, and 2 or 3 vs. 0, while considering 3 vs. 2, 2 vs. 1, and 1 vs. 0 to be too weak for this final elimination decision that is based on a mere 1/1 defeat ratio cutoff. The candidate that remains is the winner. If there is a pairwise tie in step three, use the middle two levels to resolve it, which is the same as electing the tied candidate with the greatest number of ratings strictly above one. None of the three elimination steps can eliminate all of the candidates because the elimination conditions are cycle proof. Furthermore, (with the tie breaker in place) the third step will eliminate all of the remaining candidates except one. Notice that the ballot comparisons get progressively stronger as we go from step one to step three, while the defeat ratio requirements get weaker, (from 3/1 to 2/1 to 1/1) but stay strong enough at each step to prevent cycles. Isn't that cool? Forest, It is certainly elegant and interesting. Wouldn't it be possible for step (2) to eliminate a Condorcet winner? If the method fails the Condorcet criterion, does it meet Favourite Betrayal? Does it ( like the Condorcet method Raynaud that also works by eliminating pairwise losers) fail mono-raise? http://wiki.electorama.com/wiki/Raynaud I can't make an example of it failing the Plurality criterion. Does it meet that criterion? Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Bucklin-like method meeting Favorite Betrayal and Irrelevant Ballots
My so-far nameless attempt at fixing Bucklin: *Voters fill out 4-slot ratings ballots, rating each candidate as either Top, Middle1, Middle2 or Bottom. Default rating is Bottom, signifying least preferred and unapproved. Any rating above Bottom is interpreted as Approval. If any candidate/s X has a Top-Ratings score that is higher than any other candidate's approval score on ballots that don't top-rate X, elect the X with the highest TR score. Otherwise, if any candidate/s X has a Top+Middle1 score that is higher than any other candidate's approval score on ballots that don't give X a Top or Middle1 rating, elect the X with the highest Top+Middle1 score. Otherwise, elect the candidate with the highest Approval score.* 35: A 10: A=B 30: BC 25: C Here (like SMD,TR) it elects B. Bucklin elects C Forrest Simmons wrote (28 May 2010): It seems to me that this new method would elect A, since A has the most TR (45 versus 40 for B) and the greatest total of approvals below top is only 30 (by C). Forest, The pertinent phrase in the definition is any other candidate's approval score on ballots that don't top-rate X. A does have the highest TR score (45) but can't win in the first round because on ballots that don't top-rate A (30BC, 25C) C has an approval score of 55. B's TR score is 40 and is allowed to win in the first round because on ballots that don't top-rate B (35A, 25C) the highest approval score is only 35. C's TR score is only 25 so of the candidates allowed to win in the first round B has the highest TR score and so wins. And in any case on ballots that don't top-rate C (35A, 10A=B, BC) A has an approval score of 45 so B is the only candidate that is allowed to win in the first round. Thanks for taking an interest Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] SMD,TR fails the Plurality criterion.
My previous message contained a small blunder. The corrected version is below A candidate X's maximum approval oppostion score is the approval score of the most approved candidate only on ballots on which X is not approved. In the example election I mistakenly gave A's MAO score as 11. The definition of SMD,TR: *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023530.html Chris Benham Kevin Venzke has come up with an example that shows that my Strong Minimal Defense, Top Ratings (SMD,TR) method fails the Plurality criterion,contrary to what I've claimed. 21: AC 08: BA 23: B 11: C Approval scores: A29, B31, C32 Maximum Approval Opposition scores: A23, B32, C31 Top-Ratings scores: A21, B31, C11. By the rules of SMD,TR B is disqualified because B's MAO score (of 32, C's approval score on ballots that don't approve B) is greater than B's approval score. Then A (as the undisqualified candidate with the highest TR score) wins. But since B has more first-place votes than A has total votes, or in the language of this method B's TR score is greater than A's total approval score, the Plurality criterion says that A can't win. This seems to show that compliance with my Unmanipulable Majority criterion is a bit more expensive than I thought. I still endorse SMD,TR as a good Favourite Betrayal complying method, but with less enthusiasm. (My UM criterion says that if A is a winner and on more than half the ballots is voted above B, it is impossible to make B the winner by altering any ballots on which B is voted above A without raising on them B's ranking or rating.) I was wrong to claim that compliance with Strong Minimal Defense implies compliance with the Plurality criterion. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] The general form of Quick Runoff
Kevin, This new Quick Runoff (QR) method suggestion of yours does nothing to shake my opinion that IRV is the best LNHarm method. Monotonicity: We still have an unusual monotonicity problem in that a candidate who lacks a majority over the candidate previous to him in first-preference order, may wish he had received fewer first preferences in order to sit behind a candidate that he did defeat (and who can still provide the necessary majority beatpath to the top). He may also wish he received *more* first preferences. Is it a wash? Without bothering to make an example, it seems obvious that it fails Mono-add-Plump. (It's conceivable that another way of ordering the candidates could preserve all the properties plus clone independence, but I'm not very optimistic at the moment.) Why not order the candidates by DSC (the reverse of the DSC disqualification order)? Wouldn't that version simply dominate (in terms of desirable criterion compliances) the QR you've defined (that uses the FPP order)? Compared to plain DSC it seems to just gain compliance with Condorcet(Gross) Loser in exchange for losing compliance with Irrelevant Ballots. Chris Benham Kevin Venzke wrote (22 May 2010): Hello, I realized that QR can be generalized for any number of candidates and still retain LNHarm, Plurality, and resistance to the usual type of burial strategy. To me this makes the method surprisingly good. The philosophy is to elect the candidate with the fewest first-preferences (think center-squeeze here) who has a very specific majority beatpath to the first-preference winner. Here is the new definition: 1. Rank the candidates. Truncation is allowed. Equal ranking is not planned for (but we could come up with something). 2. Label the candidates A, B, C, ... Z in descending order of first preference count. 3. Let the current leader be A. 4. While the current leader has a majority pairwise loss to the very next candidate, set the current leader to the latter candidate. (In other words step 4 must be repeated until there is no loss or no other candidates.) 5. Elect the current leader. Proof of LNHarm satisfaction: Let's say you were voting BY (retaining the meaning of the alphabetical ordering) and you consider changing your ballot to BYM. The sole effect this may have is to create a majority for ML, causing L to lose. You didn't rank L, so you didn't harm any higher preferences. (And if you had ranked L, then adding the M preference could not have created a majority ML. Also note that adding preferences cannot reverse or remove any majorities.) Who wins instead? Let's talk about burial. Typically the concern is that voters for a strong candidate will rank a weak candidate insincerely high in an effort to make a strong competitor lose. For example, you would vote AC to confuse the method into defeating B and electing A. In QR your added C preference can only help elect a candidate who was even weaker (in first preferences) than C. This makes burial a useless strategy for the largest factions. Proof of Plurality satisfaction (a second advantage over MMPO): If X has more first preferences than Y has votes total, then Y can't have a majority win over anybody and can never be the current leader. Monotonicity: We still have an unusual monotonicity problem in that a candidate who lacks a majority over the candidate previous to him in first-preference order, may wish he had received fewer first preferences in order to sit behind a candidate that he did defeat (and who can still provide the necessary majority beatpath to the top). He may also wish he received *more* first preferences. Is it a wash? In any case, getting additional second or third (etc) preferences can't hurt a candidate. QR doesn't satisfy Condorcet(gross) (i.e. a candidate with a majority over every other candidate is not guaranteed to win unless he is one of the top two candidates in first-preference order) but it does satisfy Condorcet(gross) Loser. It doesn't satisfy minimal defense in general. A candidate barred according to minimal defense can only win if he places first (since he will be unable to take the win from any other candidate) and he does not lose by a majority to second-place. (If the latter candidate is the majority's common candidate under minimal defense, then the barred candidate will lose.) It doesn't satisfy SFC generally (because a majority win is only enforced against one other candidate) but it does work when the involved candidates place first and second in some order. (If the suspected sincere CW is A, then A has a majority over B and wins immediately; if the suspected sincere CW is B, then B takes the win from A and B cannot lose it to anybody.) Fairly obviously it satisfies Majority Favorite and Majority Last Preference. It doesn't satisfy Majority for Solid Coalitions due to the possibility that the majority's first preferences are so fragmented that none of their candidates place first or second
[EM] Proposal: Majority Enhanced Approval (MEA)
Forest, This MEA method you have suggested would nearly always give the same winner as Smith//Approval (ranking), one of the methods I endorse. Where they do give different winners, would it be the case that the Smith//Approval winner is the more approved? But outside the Uncovered set? What is the most realistic example you can give of the two methods giving different winners? A feature of both methods that I am going off is that voters can be punished for failing to truncate their least preferred of the viable candidates. 49: A1A2 24: B 27: CBA1 A1 is uncovered and most approved, so both methods elect A1. But the presence of the weakly pareto-dominated clone A2 on the ballot caused the C supporters to not truncate A1. If they had done so then B would have won. This type of example is what motivated me to recently propose that a candidate's 'biggest gross pairwise score in a pairwise victory over an uncovered candidate' be used as a quasi-approval score. B then wins whether the C voters truncate A1 or not. (The other motivation was that I was looking for something that used nothing but the normal gross pairwise matrix.) I recognize that this can cause failure of mono-raise, but probably only in a complicated not very likely example. Chris Benham Forest Simmons wrote (8 May 2010): I have a proposal that uses the same pairwise win/loss/tie information that Copeland is based on, along with the complementary information that Approval is based on. It’s a simple and powerful Condorcet/Approval hybrid which, like Copeland, always elects an uncovered candidate, but without the indecisiveness or clone dependence of Copeland. I used to call it UncAAO, but for better name recognition, I’m changing the name to Majority Enhanced Approval (MEA). The method is extremely easy to understand once you get the simple concept of covering. Candidate X covers candidate Y if candidate X pairwise beats both Y and every candidate that Y beats pairwise. MEA elects the candidate A1 that is approved on the greatest number of ballots if A1 is uncovered. Otherwise it elects the highest approval candidate A2 that covers A1 if A2 is uncovered. Otherwise it elects the highest approval candidate A3 that covers A2 if A3 is uncovered. Otherwise, etc. until we arrive at an uncovered candidate An, which is elected. MEA satisfies Monotonicity, Clone Independence, Independence from Pareto Dominated Alternatives, and Independence from Non-Smith Alternatives, as well as all of the following: 1. It elects the same member of a clone set as the method would when restricted to the clone set. 2. If a candidate that beats the winner is removed, the winner is unchanged. 3. If an added candidate covers the winner, the new candidate becomes the new winner. 4. If the old winner covers an added candidate, the old winner still wins. 5. It always chooses from the uncovered set. 6. It is easy to describe: Initialize L to be an empty list. While there exists some alternative that covers every member of L, add to L the one (from among those) with the greatest approval. Elect the last candidate added to L. What other deterministic method (based on ranked ballots with truncations allowed) satisfies all of these criteria? Forest Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Scenario where IRV and Asset outperform Condorcet, Range, Bucklin, Approval.
Kristofer Munsterhjelm wrote (12 May 2010): One idea of mine, although extremely complex, would be to select the two candidates for a runoff by two Condorcet methods - one that's resistant to strategy (like Smith,IRV), and one that's not but provides better results in the honest vote case (e.g. Schulze, uncovered methods). Since the second round is honest - a two-candidate election where a majority wins is strategy-proof - it should lower the chances of ending up with a very bad candidate. If the two methods agree, the candidate would win outright. These sorts of schemes (a runoff between the winners of methods A and B) invariably fail mono-raise and are vulnerable to Pushover strategy. The voters may also end up arguing that because the two methods agree so often (if they do), there's no need to have the runoff in the first place; if the method deters organized strategy, the organized strategy wouldn't appear and so the actual runoff mechanism would appear superfluous. So the threat of a runoff (that is never needed to be held) is deterring organised strategy is somehow an argument for abolishing the threat?? A better 2-round scheme would be to have all the members of the Smith set eligible for the second round, which uses simple Approval. Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] MinMax(AWP) and Participation
Forest wrote: ..MinMax is the only commonly known Condorcet method that satisfies the following weak form of Participation: If A wins and then another ballot with A ranked unique first is added to the count, A still wins. That is Mono-add-Top, I think coined by Douglas Woodall. It is met by IRV. Beatpath, River, Ranked Pairs, etc. fail this weak participation criterion, but they do satisfy this even weaker version: If A wins and then another ballot with only A ranked is added to the count, then A still wins. That is Mono-add-Plump. Forest, Is there some method that you like or take seriously that actually fails this criterion? Chris Benham Forest Simmons wrote (21 April 2010): I don't know if Juho is still cheering for MinMax as a public proposal. I used to be against it because of its clone dependence, but now that I realize that measuring defeat strength by AWP (Approval Weighted Pairwise) solves that problem, I'm starting to warm up more to the idea. MinMax elects the candidate that suffers no defeats if there is one, else it elects the one whose maximum strength defeat is minimal. There are various ways of measuring defeat strength. James Green Armytage has advocated one called AWP as making Condorcet methods less vulnerable to strategic manipulation. If all ranked candidates on a ballot are considered approved, then the AWP strength of a defeat of B by A is the number of ballots on which A is ranked but B is not. Then more recently I was reading a paper by Joaquin Pérez in which he shows that MinMax is the only commonly known Condorcet method that satisfies the following weak form of Participation: If A wins and then another ballot with A ranked unique first is added to the count, A still wins. Beatpath, River, Ranked Pairs, etc. fail this weak participation criterion, but they do satisfy this even weaker version: If A wins and then another ballot with only A ranked is added to the count, then A still wins. Proof: First add a ballot in which no candidate is ranked. The above mentioned methods allow this, and it doesn't affect their outcome since no mention of absolute majority is made in any of them. Then raise A while leaving the other candidates unranked. This cannot hurt A since all of the above mentioned methods are monotone. Knowing that Beatpath satisfies the weaker version but not the weak version may be an inducement for voters to bullet vote candidate A to make sure that they avoid the no show paradox. But MinMax is free of this temptation; they wouldn't have to truncate the other candidates. Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Classifying 3-cand scenarios. LNHarm methods again.
Dave Ketchum wrote 17 April 2010: First, quoting Wikipedia: A Condorcet method is any single-winner election method that meets the Condorcet criterion, that is, which always selects the Condorcet winner, the candidate who would beat each of the other candidates in a run-off election, if such a candidate exists. In modern examples, voters rank candidates in order of preference. There are then multiple, slightly differing methods for calculating the winner, due to the need to resolve circular ambiguities—including the Kemeny- Young method,Ranked Pairs, and the Schulze method. Almost all of these methods give the same result if there are fewer than 4 candidates in the circularly-ambiguous Smith set and voters separately rank all of them. I have heard this complaint before, so am listening for help. WHAT should I say when I want EXACTLY what is described as Condorcet above? Dave, The Wikiipedia piece you quote doesn't say *the* Condorcet method. It says A Condorcet method... So you couuld say that, or a Condorcet-complying method. You asked Will not Condorcet attend to clones with minimum pain? Plain Condorcet won't do anything except elect a voted CW if there is one. Some Condorcet-complying methods are clone-proof and some aren't. Chris Benham On Apr 17, 2010, at 9:25 PM, Markus Schulze wrote: Hallo, Dave Ketchum wrote (18 April 2010): Why IRV? Have we not buried that deep enough? Why not Condorcet which does better with about the same voting? Why TTR? Shouldn't that be avoided if trying for a good method? TTR requires smart deciding as to which candidates to vote on. Will not Condorcet attend to clones with minimum pain? Voters can rank them together (with equal or adjacent ranks). Does not Condorcet properly attend to symmetric with a voted cycle? In my opinion, Condorcet refers to a criterion rather than to an election method. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Multiwinner Bucklin - proportional, summable (n^3), monotonic (if fully-enough ranked)
Jameson Quinn wrote (26 March 2010): snip Right now, I think MCV - that is, two-rank, equality-allowed Bucklin, with top-two runoffs if no candidate receives a majority of approvals in those two ranks - is my favorite proposal for practical implementation. snip Jameson, What does MCV stand for? Does top-two runoffs mean a second trip to the polls? How are the candidates scored to determine the top two? Is it based on the candidates' scores after the second Bucklin round? Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Smith, FPP fails Minimal Defense and Clone-Winner
Robert Bristow-Johnson wrote (9 March 2010): snip so, keeping RP, Schulze in mind for later, what would be a good scheme for resolving cycles by use of elimination of candidates? what would be a good (that is resistant to more anomalies) and simple method to identify the weakest candidate (in the Smith set) to eliminate and run the beats-all tabulation again? i'm not saying elimination is a good way to do it, but it might be easier to sell to neanderthal voters. r b-j I recommend Smith//Approval(ranking): *Voters rank from the top candidates they approve. Equal-ranking is allowed. Interpreting being ranked above at least one other candidate as approval, elect the most approved member of the Smith set (the smallest non-empty set S of candidates that pairwise beat all the outside-S candidates).* I don't think this is very hard to explain or sell. Who do you think should win this election? 25: AB 26: BC 23: CA 26: C CA 75-25, AB 49-26, BC 51-49 Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Simple monotonicity question
Kristofer Munsterhjelm wrote: Does nonmonotonicity in three-candidate IRV only happen when the Condorcet winner is eliminated? No. 47: ACB 26: BA 02: CAB 25: CB There is no Condorcet winner. IRV elects A but if the two CAB ballots are changed to ACB then there is still no Condorcet winner and now IRV elects B, a failure of mono-raise. 49: ACB 26: BA 25: CB Chris Benham __ Yahoo!7: Catch-up on your favourite Channel 7 TV shows easily, legally, and for free at PLUS7. www.tv.yahoo.com.au/plus7 Election-Methods mailing list - see http://electorama.com/em for list info
[EM] good method ? , was IRV ballot pile count (proof of closed form)
Rob LeGrand wrote (11 Feb 2010): snip 35:A 32:BC 33:C, by which I mean 35:AB=C 32:BCA 33:CA=B. In this example, C is the Condorcet winner even though C does not have a majority over B. I can see how this example could be seen as an embarrassment to the Condorcet criterion, in that a good method might not choose C as the winner. end quoted message Rob, Well I can't. Electing A would be a violation of the Minmal Defense criterion, and electing B would violate Woodall's Plurality criterion and Condorcet Loser. What good method do you have in mind that might not elect C? And what's good about it? Chris Benham Election-Methods mailing list - see http://electorama.com/em for list info
[EM] IRV vs Plurality
Juho wrote (26 Jan 2010): snip It may well be that this method can be characterized as not fully Condorcet and Approval strategy added. I'm not quite sure that the intended idea of mostly Condorcet with core support rewarded (= do what the IRV core support idea is supposed to do) works well enough to justify this characterization and the use of this method (when core support is required). There is however some tendency to reward the large parties or other core support (as intended) and the behaviour is quite natural with some more common sets of votes. snip Juho, I don't see the IRV core support idea as a serious part of IRV's motivation. Rather I see it as reasonable propaganda to on the one hand offer some vague philosophical excuse for not meeting the Condorcet criterion, and on the other reassure those who are wary of too radical a change (from Plurality) that this method will not elect a candidate with very few first preferences. The proper criterion that I see it as being most closely positively linked to is Mutual Dominant Third, a weakened version of Condorcet that says that if more than a third of the voters vote all the members of subset S of candidates above all the non-member candidates and all the members of S pairwise beat all the non-members, then the winner must come from S. Also of course it seeks to put a positive spin on the fact that the candidate with the fewest first preferences can't win, even if that candidate is the big pairwise beats-all winner. snip 51: ABC 41: BCA 08: CAB BA 61.5 - 59, BC 112.5 - 12, AC 76.5 - 53 51% voted A as their unique favourite and 59% voted A above B, and yet B wins. Yes, and I believe there are more criteria that the method fails. We should however from some point of view be happy since the method elected B that seems to have 92% core support (maybe this is how I defined core support in this method). snip Defining as you do core support as approval, what is your objection to simpler methods that don't allow ranking among unapproved candidates (and so just interpret ranking above bottom as approval) such as the Smith//Approval(ranking) method I endorse? Or if you think that it is justified for a candidate with a very big approval score to beat a majority favourite with less approval, why not simply promote the plain Approval method? Chris Benham __ Yahoo!7: Catch-up on your favourite Channel 7 TV shows easily, legally, and for free at PLUS7. www.tv.yahoo.com.au/plus7 Election-Methods mailing list - see http://electorama.com/em for list info
[EM] IRV vs Plurality
Juho wrote (25 Jan 2010): I reply to myself since I want to present one possible simple method that combines Condorcet and added weight to first preferences (something that IRV offers in its own peculiar way). Let's add an approval cutoff in the Condorcet ballots. The first approach could be to accept only winners that have some agreed amount of approvals. But I'll skip that approach and propose something softer. A clear approval cutoff sounds too black and white to me (unless there is already some agreed level of approval that must be met). The proposal is simply to add some more strength to opinions that cross the approval cutoff. Ballot ABCD would be counted as 1 point to pairwise comparisons AB and CD but some higher number of points (e.g. 1.5) to comparisons AC, AD, BC and BD. This would introduce some approval style strategic opportunities in the method but basic ranking would stay as sincere as it was. I don't believe the approval related strategic problems would be as bad in this method as in Approval itself. snip The some higher number of points (e.g. 1.5) looks arbitrary and results in the method failing Majority Favourite, never mind Condorcet etc. 51: ABC 41: BCA 08: CAB BA 61.5 - 59, BC 112.5 - 12, AC 76.5 - 53 51% voted A as their unique favourite and 59% voted A above B, and yet B wins. Chris Benham __ Yahoo!7: Catch-up on your favourite Channel 7 TV shows easily, legally, and for free at PLUS7. www.tv.yahoo..com.au/plus7 Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Strong Minmal Defense, Top Ratings
In a recent EM post in another thread, I defined and recommended the Strong Minimal Defense, Top Ratings method (that I first proposed in 2008) as the best of the methods that meet the Favourite Betrayal criterion, and also the best 3-slot ballot method: *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* I gather from one off-list response that this sentence of mine could have been more clear: 'Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so the voters have a less strong incentive to truncate..' I neglected to mention that I think it is desirable that after top-voting X, ranking Y below X (but above bottom) should be about equally likely to help X as to harm X. This implies that if one of the the two LNhs are failed, it is desirable that the other is also. MCA/Bucklin meets Later-no-Help while failing Later-no-Harm. The voters have a big incentive to truncate, and to equal-rank at the top, so with strategic voters it tends to look like plain Approval. In SMD,TR after top-rating X, middle-rating Y may harm X or may help X. As discussed in 2008, it fails Mono-add-Top (and so Participation). 8: C 3: F 2: XF 2: YF 2: ZF F wins after all other candidates are disqualified, but if 2 FC ballots are added C wins. Of course it is far from uniquely bad in that respect. A big plus for it is that it is virtually alone in meeting my proposed Unmanipulable Majority strategy criterion: Regarding my proposed Unmanipulable Majority criterion: *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.* http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023530.html In common with MCA it meets mono-raise (aka ordinary monotonicity) and a 3-slot ballot version of Majority for Solid Coaltions, which says that if majority of the voters rate a subset S of the candidates above all the outside-S candidates, the winner must come from S. From the post that introduced SMD,TR: It is more Condorcetish and has a less severe later-harm problem than MCA, Bucklin, or Cardinal Ratings (aka Range, Average Rating, etc.) 40: AB 35: B 25: C Approval scores: A40, B75, C25 Approval Opp.: A35, B25, C75 Top-ratings scores: A40, B35, C25 They elect B, but SMD,TR elects the Condorcet winner A. Chris Benham __ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
Dave Ketchum wrote (18 Jan 2010): In response I will pick on LNH for not being a serious reason for rejecting Condorcet - that such failure can occur with reasonable voting choices for which the voter knows what is happening. Quoting from Wikipedia: For example in an election conducted using the Condorcet compliant method Ranked pairs the following votes are cast: 49: A 25: B 26: CB B is preferred to A by 51 votes to 49 votes. A is preferred to C by 49 votes to 26 votes. C is preferred to B by 26 votes to 25 votes. There is no Condorcet winner and B is the Ranked pairs winner. Suppose the 25 B voters give an additional preference to their second choice C. The votes are now: 49: A 25: BC 26: CB C is preferred to A by 51 votes to 49 votes. C is preferred to B by 26 votes to 25 votes. B is preferred to A by 51 votes to 49 votes. C is now the Condorcet winner and therefore the Ranked pairs winner. By giving a second preference to candidate C the 25 B voters have caused their first choice to be defeated. Pro-A is about equal strength with anti-A. For this it makes sense for anti-A to give their side the best odds with the second vote pattern, not caring about LNH (B and C may compete with each other, but clearly care more about trouncing A). snip Dave, Your assumption that B and C may compete with each other, but clearly care more about trouncing A is based on what? The ballots referred to contain only the voters' rankings, with no indications about their relative preference strengths. If you read my entire post you will see that in it I endorse three methods, one of which is a Condorcet method. Chris Benham __ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] IRV vs Plurality ( Kristofer Munsterhjelm )
Kristofer Munsterhjelm wrote (17 Jan 2010): To me, it seems that the method becomes Approval-like when (number of graduations) is less than (number of candidates). When that is the case, you *have* to rate some candidates equal, unless you opt not to rate them at all. That won't make much of a difference when the number of candidates is huge (100 or so), but then, rating 100 candidates would be a pain. I'd say it would be better to just have plain yes/no Approval for a first round, then pick the 5-10 most approved for a second round (using Range, Condorcet, whatever). Or use minmax approval or PAV or somesuch, as long as it homes in on the likely winners of a full vote. Simply using plain Approval to reduce the field to the top x point scorers who then compete in the final round seems unsatifactory to me because of the Rich Party incentive (clone problem) for parties to field x candidates; and because of the tempting Push-over (turkey raising) strategy incentive. Chris Benham __ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
Abd Lomax wrote (17 Jan 2010): snip Chris is Australian, and is one of a rare breed: someone who actually understands STV and supports it for single-winner because of LNH satisfaction. Of course, LNH is a criterion disliked by many voting system experts, and it's based on a political concept which is, quite as you say, contrary to sensible negotiation process. snip I endorse IRV (Alternative Vote, with voters able to strictly rank from the top however many candidates they choose) as a good method, much better than Plurality or TTR, and the best of the methods that are invulnerable to Burial and meet Later-no-Harm. Some of us see elections as primarily a contest and not a negotiation process. I endorse IRV because it has a maximal set of (what I consider to be) desirable criterion compliances: Majority for Solid Coalitions (aka Mutual Majority) Woodall's Plurality criterion Mutual Dominant Third Condorcet Loser Burial Invulnerability Later-no-Harm Later-no-Help Mono-add-Top Mono-add-Plump (implied by mono-add-top) Mono-append Irrelevant Ballots Clone-Winner Clone-Loser (together these two add up to Clone Independence) As far as I can tell, the only real points of dissatisfaction with IRV in Australia are (a) that in some jurisdictions the voter is not allowed to truncate (on pain of his/her vote being binned as invalid) and (b) that it isn't multi-winner PR so that minor parties can be fairly represented. I gather the Irish are also reasonably satisfied with it for the election of their President. snip I've really come to like Bucklin, because it allows voters to exercise full power for one candidate at the outset, then add, *if they choose to do so*, alternative approved candidates. snip The version of Bucklin Abd advocates (using ratings ballots with voters able to give as many candidates they like the same rating and also able to skip slots) tends to be strategically equivalent to Approval but entices voters to play silly strategy games sitting out rounds. It would be better if 3-slot ballots are used, in which case it is the same thing as (one of the versions of) Majority Choice Approval (MCA). IMO the best method that meets Favourite Betrayal (and also the best 3-slot ballot method) is Strong Minimal Defence, Top Ratings: *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* Unlike MCA/Bucklin this fails Later-no-Help (as well as LNHarm) so the voters have a less strong incentive to truncate. Unlike MCA/Bucklin this meets Irrelevant Ballots. In MCA candidate X could be declared the winner in the first round, and then it is found that a small number of voters had been wrongly excluded and these new voters choose to openly bullet-vote for nobody (perhaps themselves as write-ins) and then their additional ballots raise the majority threshold and trigger a second round in which X loses. I can't take seriously any method that fails Irrelevant Ballots. Compliance with Favourite Betrayal is incompatible with Condorcet. If you are looking for a relatively simple Condorcet method, I recommend Smith//Approval (ranking): *Voters rank from the top candidates they approve. Equal-ranking is allowed. Interpreting being ranked above at least one other candidate as approval, elect the most approved member of the Smith set (the smallest non-empty set S of candidates that pairwise beat all the outside-S candidates).* Chris Benham __ See what's on at the movies in your area.. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
Abd ul-Rahman Lomax wrote (14 Jan 2010): snip Why does Kathy elsewhere defend Top Two Runoff which isn't monotonic? This opinion, stated as fact, is false. Top Two Runoff is a two-step system, and monotonicity doesn't refer to such. It refers to the effect of a vote on a single ballot as to the result of that ballot only. A vote for a candidate on a primary ballot in TTR will always help the candidate supported to make it either to a majority and a win, or to make it into the runoff. It never hurts that candidate. snip A vote for any candidate X in any given IRV counting round will likewise help X to a majority win or to make it into the next round. The contention that a two-step system (meaning requiring voters to make two trips to the polls) to elect a single candidate isn't allowed to be judged in aggregate is absurd. snip Did supporters of the Lizard vote for the Wizard in order to create the Lizard vs. Wizard election in Louisiana? I rather doubt it. But this wouldn't create a monotonicity violation, and the problem is created by eliminations, it doesn't exist with repeated balloting. snip With repeated balloting there are no eliminations? As I undersatnd it, in Top Two Runoff all but the top two first-round vote getters are eliminated if no candidate gets more than half the votes in the first round. Chris Benham __ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Two simple alternative voting methods that are fairer than IRV/STV and lack most IRV/STV flaws
than satisfying Majority Favorite? Why does Kathy elsewhere defend Top Two Runoff which isn't monotonic? Chris Benham __ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] IRV vs Plurality
Dave Ketchum wrote (9 Jan 2010): For a quick look at IRV: 35A, 33BC, 32C A wins for being liked a bit better than B - 3533. That C is liked better than A is too trivial for IRV to notice - 6535. Let one BC voter change to C and C would win over A - 6535. Let a couple BC voters switch to A and C would win over A - 6337. Point is that IRV counting often ignores parts of votes. Dave Ketchum Yes. The implicit assumption seems to be that ignoring parts of votes is always a pure negative but not doing so can cause failure of Later-no-Harm and Later-no-Help, and vulnerability to Burial. All Condorcet methods fail those criteria, while IRV meets them. Note that I wrote that IRV is my favourite of the methods that are invulnerable to Burial strategy and meet Later-no-Harm. I didn't write that it was necessarily preferable to to all of the methods that meet the Condorcet criterion. Chris Benham __ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] IRV vs Plurality
Kathy Dopp wrote (11 Jan 2010): snip Plurality is far better than IRV for many many reasons including: 1. preserves the right to cast a vote that always positively affects the chances of winning of the candidate one votes for 2. allows all voters the right to participate in the final counting round in the case of top two runoff or primary/general elections snip IRV satisfies both of these. Regarding the first,assuming that the candidate one votes for refers to the candidate the voter top-ranks, then top-ranking X in an IRV election has the same positive effect on X's chance of winning as does voting for X in a Plurality election. It is true that sometimes in an IRV election a subset of X's sincere supporters may be able to do better for X by top-ranking some non-X, whereas in Plurality the best strategy for all of X's supporters is always just to vote for X; but that is different. IRV meets Mono-add-top, which means that a voter who top-ranks X would never have done better for X by staying home. Having arrived at the voting booth, the X supporter's overwhelmingly best probabilistic IRV strategy is to top-rank X. Regarding Kathy's second point, IRV voters should be allowed to strictly rank from the top as many candidates as they wish. The voter is then free to ensure that s/he participates in the final counting round by simply ranking all the candidates (or alternatively if the likely front-runners are known then just make it very likely by ranking among them). Chris Benham __ See what's on at the movies in your area. Find out now: http://au.movies.yahoo.com/session-times/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] IRV is best method meeting 'later no harm'?
Steve Eppley wrote (26 Nov 2009): Can it be said that Later No Harm (LNH) is satisfied by the variation of IRV that allows candidates to withdraw from contention after the votes are cast? No. Take this classic (on EM) scenario: 49: A 24: B 27: CB A is the normal IRV winner, but in the variation you describe C presumably withdraws causing B to win. 49: A 24: BC 27: CB If the B supporters instead of truncating vote BC then C wins. Assuming C accepts the win the B voters have caused B to lose by not truncating, a clear failure of Later-no-Harm. Steve wrote: Since IRV is said to satisfy LNH, then one must say Plurality Rule satisfies LNH too, because Plurality Rule can be viewed as just a variation of IRV with a smaller limit (one candidate per voter). Yes, and I did. I listed FPP (First-Preference Plurality or more traditionally First Past the Post) as a method that meets Later-no-Harm. I understand that in the US the Alternative Vote is called IRV, but that sometimes various inferior approximations are given the same label. Chris Benham __ Win 1 of 4 Sony home entertainment packs thanks to Yahoo!7. Enter now: http://au.docs.yahoo.com/homepageset/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Anyone got a good analysis on limitations of approval and range voting?
Robert Bristow-Johnson wrote (9 Nov 2009): Of course IRV, Condorcet, and Borda use different methods to tabulate the votes and select the winner and my opinion is that IRV (asset voting, i might call it commodity voting: your vote is a commodity that you transfer according to your preferences) is a kabuki dance of transferred votes. and there is an *arbitrary* evaluation in the elimination of candidates in the IRV rounds: 2nd- choice votes don't count for shit in deciding who to eliminate (who decided that? 2nd-choice votes are as good as last-choice? under what meaningful and consistent philosophy was that decided?), then when your candidate is eliminated your 2nd-choice vote counts as much as your 1st-choice. Regarding IRV's philosophy: each voter has single vote that is transferable according to a rule that meets Later-no-Harm, Later-no-Help and Majority for Solid Coalitions. I rate IRV (Alternative Vote with unlimited strict ranking from the top) as the best of the single-winner methods that meet Later-no-Harm. Chris Benham __ Win 1 of 4 Sony home entertainment packs thanks to Yahoo!7. Enter now: http://au.docs.yahoo.com/homepageset/ Election-Methods mailing list - see http://electorama.com/em for list info
[EM] 'Shulze (Votes For)' definition?
Marcus, I have some questions about your draft (dated 23 June 2009) Shulze method paper, posted: http://m-schulze.webhop.net/schulze1.pdf On page 13 you define some of the ways of measuring defeat strengths, two of which are Votes For and Votes Against: snip Example 5 ( then the strength is measured primarily by the absolute number N[e,f] of votes for candidate e. (N[e,f],N[f,e]) for (N[g,h],N[h,g]) if and only if at least one of the following conditions is satisfied: 1. N[e,f] N[g,h]. 2. N[e,f] = N[g,h] and N[f,e] N[h,g]. Example 6 (votes against): When the strength of the pairwise defeat ef is measured by votes against, then the strength is measured primarily by the absolute number N[f,e] of votes for candidate f. (N[e,f],N[f,e]) against (N[g,h],N[h,g]) if and only if at least one of the following conditions is satisfied: 1. N[f,e] N[h,g]. 2. N[f,e] = N[h,g] and N[e,f] N[g,h]. snip I am a little bit confused as to the exact meaning of the phrase the absolute number ..of votes for candidate E. Does the number of votes for E mean 'the number of ballots on which E is ranked above at least one other candidate'? Or does it mean something that can be read purely from the pairwise matrix? Does it mean 'the sum of all the entries in the pairwise matrix that represent pairwise votes for E'? Do the two methods 'Schulze(Votes For)' and 'Shulze(Votes Against)' meet Independence of Clones? I look forward to hearing your clarification. Chris Benham votes for): When the strength of the pairwise defeat ef is measured by votes for, __ Find local businesses and services in your area with Yahoo!7 Local. Get started: http://local.yahoo.com.au Election-Methods mailing list - see http://electorama.com/em for list info
[EM] 'Shulze (Votes For)' definition?
Kevin, Or does it mean something that can be read purely from the pairwise matrix? It's the latter, read from the matrix. Absolute number is in contrast to using margin or ratio. Thanks for that, but it isn't the concept of absolute number that I'm having trouble with. What I don't understand is the difference between winning votes (which I'm familiar with) and votes for, as they are both defined on page 13 of Marcus Shulze's paper, pasted below. http://m-schulze.webhop.net/schulze1.pdf snip Example 3 ( by winning votes, then the strength is measured primarily by the absolute number N[e,f] of votes for the winner of this pairwise defeat. snip Example 5 ( votes for candidate e. votes for): When the strength of the pairwise defeat ef is measured by votes for, then the strength is measured primarily by the absolute number N[e,f] of winning votes): When the strength of the pairwise defeat ef is measured snip Chris Benham __ Find local businesses and services in your area with Yahoo!7 Local. Get started: http://local.yahoo.com.au Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Electowiki relicensed to Creative Commons Share Alike 3.0
In the Electowiki article on the River method, none of these links work properly: * First proposal * * slight refinement * * More concise definition. In this last version, River is defined very similarly to ranked pairs. * * Example using 2004 baseball scores. This shows how a * 14-candidate election winner can be determined much more * quickly using River than with RP or Schulze. * Early criticism of the River method. This shows that the River * method violates mono-add-top and mono-remove-bottom One is broken and the rest go to the wrong EM post. http://wiki.electorama.com/wiki/River Also, some of my EM posts in the Electorama archive have links to other EM posts which also go to the wrong one. Chris Benham Access Yahoo!7 Mail on your mobile. Anytime. Anywhere. Show me how: http://au.mobile.yahoo.com/mail Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet/Range DSV
Jameson, Sorry to be so tardy in replying. That is not a bad suggestion; I like both systems. Yours gives less of a motivation for honest rating: In most cases, it makes A100 B99 C0 equivalent to A100 B51 C0. No, mine gives more motivation for honest rating (in the sense that it gives less incentive for dishonest rating). If A, B, C are the three Smith-set members then it makes both A100, B99, C0 and A100, B51, C0 equivalent to A100, B100, C0. I guess you'd give exactly half an approval if B were at exactly 50? Yes. 49: A100, B0, C0 24: B100, A0, C0 27: C100, B80, A0 More than half the voters vote A not above equal-bottom and below B, and yet A wins. True. Yet B could win if the C voters rated B 99, which would still be Condorcet-honest. That isn't really in principle relevant because your suggested method doesn't guarantee to a section of the voters comprising more than half who rate/rank A bottom that they can ensure that A loses while still expressing all their sincere pairwise preferences. 4999: A100, B0, C0 2500: B100, A0, C0 2501: C100, B99, A0 BA 5001- 4999, AC, CB. In this modified version of my demonstration that your suggested method fails Minimal Defense, the majority that prefer B to A cannot ensure that B loses and still be Condorcet-honest. Anyway, the main motivations for a DSV-type proposal like this is to make it really rare for voters to have enough information to strategize without it backfiring. I think that including full range information (that is, my proposal as opposed to yours) makes the voter's analysis harder, and so makes the system more resistant to strategy. I don't think the type of examples I've given would be really rare, and in them I don't think the C supporters have to very well-informed or clever to work out that their candidate can't beat A and so they have incentive to falsely vote B (at least) equal to their favourite. Favorite Betrayal in this case means, honest ABC voters who know that A's losing and that CBA and ACB votes are both relatively common, can vote BAC to cause a Condorcet tie and perhaps get B to win ... Not necessarily, no. You seem to be assuming that Favourite Betrayal strategy is only about falsely creating a Condorcet tie when one's favourite isn't the (presumed to be) sincere Condorcet winner. It can also be the case that the strategist fears that if she votes sincerely there will be no Condorcet winner, so she order-reverse compromises to try to make her compromise the voted Condorcet winner. Chris Benham Jameson Quinn wrote (26 June 2009) : This Condorcet-Range hybrid you suggest seems to me to inherit a couple of the problems with Range Voting. Fair enough. It fails the Minimal Defense criterion. 49: A100, B0, C0 24: B100, A0, C0 27: C100, B80, A0 More than half the voters vote A not above equal-bottom and below B, and yet A wins. True. Yet B could win if the C voters rated B 99, which would still be Condorcet-honest. Also I don't like the fact that the result can be affected just by varying the resolution of ratings ballots used, an arbitrary feature. I think it would be better if the method derived approval from the ballots, approving all candidates the voter rates above the voter's average rating of the Smith set members. That is not a bad suggestion; I like both systems. Yours gives less of a motivation for honest rating: In most cases, it makes A100 B99 C0 equivalent to A100 B51 C0. I guess you'd give exactly half an approval if B were at exactly 50? Anyway, the main motivations for a DSV-type proposal like this is to make it really rare for voters to have enough information to strategize without it backfiring. I think that including full range information (that is, my proposal as opposed to yours) makes the voter's analysis harder, and so makes the system more resistant to strategy. Under honest range votes, it also helps improve the utility. For strategies which don't change the content of the Smith set, it does very well on other criteria, fulfilling Participation, Consistency, and Local IIA. Sorry, I wasn't clear. If the content of the smith set DOES change, this method fails all those criteria. See below for argument of why that's not too bad. And because it uses Range ballots as an input but encourages more honest voting than Range,.. That is more true of the automated approval version I suggested, and also it isn't completely clear-cut because Range meets Favourite Betrayal which is incompatible with Condorcet. Favorite Betrayal in this case means, honest ABC voters who know that A's losing and that CBA and ACB votes are both relatively common, can vote BAC to cause a Condorcet tie and perhaps get B to win (if A would win that tie, then A would be winning already, so they can't get their favorite through betrayal. In other words, at least it's monotonic
[EM] Condorcet/Range DSV
Jameson, This Condorcet-Range hybrid you suggest seems to me to inherit a couple of the problems with Range Voting. It fails the Minimal Defense criterion. 49: A100, B0, C0 24: B100, A0, C0 27: C100, B80, A0 More than half the voters vote A not above equal-bottom and below B, and yet A wins. Also I don't like the fact that the result can be affected just by varying the resolution of ratings ballots used, an arbitrary feature. I think it would be better if the method derived approval from the ballots, approving all candidates the voter rates above the voter's average rating of the Smith set members. For strategies which don't change the content of the Smith set, it does very well on other criteria, fulfilling Participation, Consistency, and Local IIA. The criteria you mention only apply (as a strict pass/fail test) to voting methods, not strategies (and have nothing to do with strategy). We know that Condorcet is incompatible with Participation (and so I suppose also with the similar Consistency). I don't see how a method that fails Condorcet Loser can meet Local IIA. And because it uses Range ballots as an input but encourages more honest voting than Range,.. That is more true of the automated approval version I suggested, and also it isn't completely clear-cut because Range meets Favourite Betrayal which is incompatible with Condorcet. Chris Benham Jameson Quinn wrote (25 June 2009) wrote: I believe that using Range ballots, renormalized on the Smith set as a Condorcet tiebreaker, is a very good system by many criteria. I'm of course nothttp://lists.electorama.com/pipermail/election-methods-electorama.com/2005-January/014469.htmlthe first one to propose this method, but I'd like to justify and analyze it further. I call the system Condorcet/Range DSV because it can be conceived as a kind of Declared Strategy Voting system, which rationally strategizes voters' ballots for them assuming that they have correct but not-quite-complete information about all other voters. Let me explain. I have been looking into fully-rational DSV methods using Range ballots both as input and as the underlying method in which strategies play out. It turns out to be impossible, as far as I can tell, to get a stable, deterministic, rational result from strategy when there is no Condorcet winner. (Assume there's a stable result, A. Since A is not a cond. winner, there is some B which beats A by a majority. If all BA voters bullet vote for B then B is a Condorcet winner, and so wins. Thus there exists an offensive strategy. This proof is not fully general because it neglects defensive strategies, but in practice trying to work out a coherent, stable DSV which includes defensive strategies seems impossible to me.) Note that, on the other hand, there MUST exist a stable probabilistic result, that is, a Nash equilibrium. Let's take the case of a 3-candidate Smith set to start with. (This simplifies things drastically and I've never seen a real-world example of a larger set.) In the Nash equilibrium, all three candidates have a nonzero probability of winning (or at least, are within one vote of having such a probability). Voters are dissuaded from using offensive strategy by the real probability that it would backfire and result in a worse candidate winning. This Nash equilibrium is in some sense the best result, in that all voters have equal power and no voter can strategically alter it. However, it is both complicated-to-compute and unnecessarily probabilistic. Forest Simmons has proposed an interesting methodhttp://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011028.htmlfor artificially reducing the win probability of the less-likely candidates, but this method increases computational complexity without being able to reach a single, fully stable result. (Simmons proposed simply selecting the most-probable candidate, which is probably the best answer, but it does invalidate the whole strategic motivation). There's an easier way. Simply assume that any given voter has only near-perfect information, not perfect information. That is, each voter knows exactly which candidates are in the Smith set, but makes an ideosyncratic (random) evaluation of the probability of each of those candidates winning. That voter's ideal strategic ballot is an approval style ballot in which all candidates above their expected value are rated at the top and all candidates below at the bottom. However, averaging over the different ballots they'd give for different subjective win probabilities, you get something very much like a range ballot renormalized so that there is at least one Smith set candidate at top and bottom. (It's not exactly that, the math is more complex, especially when the Smith set is bigger than 3; but it's a good enough approximation and much simpler than the exact answer). Let's look at a few scenarios to see how this plays out
[EM] voting strategy with rank-order-with-equality ballots
Warren, How true is it that approval-style voting is strategic for Schulze? Not very true. It depends on the voter's information and sincere ratings. Schulze, being a Condorcet method fails Favourite Betrayal. Is Schulze with approval-style ballots a better or worse voting system than plain approval? If approval-style ballots are compelled than Schulze is the same as plain Approval. If they are merely allowed (as Marcus Schulze and other proponents favour) then in my opinion it is better than Approval. In the zero-information case, the voter with a big enough gap in hir sincere ratings does best to rank all the candidates above the gap equal top and to strictly rank all those below it (random-filling if necessary in the absence of a sincere full ranking). I find it preferable that the zero-info. strategy for a ranked-ballot method be either full sincere ranking regardless of relative ratings (as in IRV and Margins) or sincere ranking above the big ratings gap and truncation below it (as in Smith//Approval). By Shulze I have been meaning Shulze(Winning Votes), the 'standard version' favoured by Marcus himself and other proponents. In January this year I suggested a different version I prefer: http://lists.electorama.com/pipermail/election-methods-electorama.com/2009-January/023959.html Chris Benham Warren Smith wrote (8 June 2009): One problem is nobody really has a good understanding of what good strategy is. If one believes that range voting becomes approval voting in the presence of strategic voters (often, anyhow)... One might similarly speculate that strategic voters in a system such as Schilze beatpaths ALLOWING ballots with both and = (e.g. AB=C=DE=F is a legal ballot) usually the strategic vote is approval style i.e. of form A=B=CD=E=F, say, with just ONE . One might then speculate that Schulze, just like range, then becomes equivalent to approval voting for strategic voters. Well... how true or false is that? Is Schulze with approval-style ballots a better or worse voting system than plain approval? How true is it that approval-style voting is strategic for Schulze? I'd like to hear people's ideas on this question. (And not necessarily just for Schulze -- substitute other methods too, if you prefer.) The trouble is, range voting is simple. Simple enough that you can reach a pretty full understanding of what strategic range voting is. (Which is not at all trivial, but it can pretty much be done.) In contrast, a lot of Condorcet systems including Schulze are complicated. Complicated enough that making confident statements about their behavior with strtagic voters (or even undertsnading what strtagy IS) is hard. Frankly, I've heard various vague but confident claims about strategy for Schulze the like, and my impression is those making the claims know very little about what they are talking about. I also know very little on this, the difference is I admit it :) Need a Holiday? Win a $10,000 Holiday of your choice. Enter now.http://us.lrd.yahoo.com/_ylc=X3oDMTJxN2x2ZmNpBF9zAzIwMjM2MTY2MTMEdG1fZG1lY2gDVGV4dCBMaW5rBHRtX2xuawNVMTEwMzk3NwR0bV9uZXQDWWFob28hBHRtX3BvcwN0YWdsaW5lBHRtX3BwdHkDYXVueg--/SIG=14600t3ni/**http%3A//au.rd.yahoo.com/mail/tagline/creativeholidays/*http%3A//au.docs.yahoo.com/homepageset/%3Fp1=other%26p2=au%26p3=mailtagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] voting strategy with rank-order-with-equality ballots
Kevin, I have found that Schulze(wv) had little favorite betrayal incentive. In simulations I mentioned in June 05, out of 50,000 trials, Schulze(wv) showed incentive 7 times, compared to 251 for Schulze(margins), 363 for Condorcet//Approval, and 625 for my erroneous interpretation of ERBucklin(whole). What was this erroneous interpretation? How can a method that meets Favourite Betrayal, such as ER-Bucklin(whole) ever show favourite betrayal incentive? Chris Benham Kevin Venzke wrote (9 June 2009): Hello, I think in Schulze(wv) and similar, decent methods, you shouldn't rank the worse of two frontrunners or below. I don't think that's a big problem though. I have found that Schulze(wv) had little favorite betrayal incentive. In simulations I mentioned in June 05, out of 50,000 trials, Schulze(wv) showed incentive 7 times, compared to 251 for Schulze(margins), 363 for Condorcet//Approval, and 625 for my erroneous interpretation of ERBucklin(whole). The simulation worked by examining the effects of introducing a strict ranking between two candidate ranked tied at the top. So a method showed favorite betrayal incentive when introducing a strict ranking AB moved the win to one of these candidates from a third candidate. You can look at incentive to compress at the top, but it's not as informative. There is compression incentive where introducing the AB strict ranking moves the win e.g. from B to a third candidate. This happened hundreds of times for the methods I looked at (1200 for ICA). I guess you could look at the odds that a strict ranking will help or hurt compared to an equal ranking, overall. I'm not sure that would be very informative either though. For one thing, it would only tell you about the zero-info case. And it wouldn't consider utility, which should be important: Whether or not you should compress at the top probably depends on how much you like those candidates compared to the other candidates. Kevin Venzke Need a Holiday? Win a $10,000 Holiday of your choice. Enter now.http://us.lrd.yahoo.com/_ylc=X3oDMTJxN2x2ZmNpBF9zAzIwMjM2MTY2MTMEdG1fZG1lY2gDVGV4dCBMaW5rBHRtX2xuawNVMTEwMzk3NwR0bV9uZXQDWWFob28hBHRtX3BvcwN0YWdsaW5lBHRtX3BwdHkDYXVueg--/SIG=14600t3ni/**http%3A//au.rd.yahoo.com/mail/tagline/creativeholidays/*http%3A//au.docs.yahoo.com/homepageset/%3Fp1=other%26p2=au%26p3=mailtagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Beatpath GMC compliance a mistaken standard?
Kevin, You wrote (25 Jan 2009): I think there ought to be a clear distinction between criteria whose violation is absurd no matter what the circumstances, and criteria whose violation is absurd due to other available options. I don't see why (particularly). There are very few (named) criteria whose failure I'd call absurd no matter what. Of those criteria, which is the one you consider to be the least absurd? (Or if you can't say, just name some.) Does your question mean that this really is how you view the difference between CDTT and Mutual Majority, is in terms of the candidates of the winning set sharing a probability pie? Not exactly. No-one has ever suggested MM,Random Ballot as a good method and few have suggested that sometimes the clearly most appropriate winner is not in the MM set (as I have regarding the CDTT set). I think that either isn't relevant or doesn't help your case. Then you can regard that as a rhetorical aside. To answer your question again I would say that way of putting it seems too mild to me, but I can't see that it's irrational. The question is about why you view MM's behavior as qualitatively different from CDTT's behavior, when in practice, in a real method, it's exactly the same behavior. In a previous message I think I made it clear that I don't accept that it is exactly the same behavior. [I don't accept that 'being tossed out of the favoured (not excluded from winning) set' is exactly the same phenomenon as 'being joined by others in the favoured set'.] Well, supposing that the public decided to accept a method that failed a positional criterion, I guess at that time I would drop that criterion. Does that mean that you think all positional criteria have no value other than to appease misguided members of the public? Hypothetically if the public were willing to accept any method I would propose to them, and not question any of its results, then I wouldn't care about appearances. I would just give them the method that I felt would perform the best. In this context, what do you mean by appearances? How can a method that you feel performs the best have (in your eyes) anything wrong with its appearance? Chris Benham Hi Chris, --- En date de : Ven 23.1.09, Chris Benham cbenha...@yahoo.com.au a écrit : I can't see what's so highly absurd about failing mono-append. It's basically a limited case of mono-raise, and one that doesn't seem especially more important. Is it absurd to fail mono-raise? The absurdity of failing mono-append is compounded by the cheapness of meeting it. As with mono-add-plump the quasi-intelligent device is given simple and pure new information. Being confused by it is simply unforgivable *stupidity* on the part of the quasi-intelligent device. I find it unclear how to decide whether something is unforgivably stupid in your view, or instead mitigated by something like this: Regards mono-raise, I would say that failing it is obviously 'positionally absurd' and 'pairwise absurd' but perhaps not 'LNH absurd'. We know that it isn't absurd in the sense that mono-add-plump and mono-append is, because it is failed by a method that has a maximal set of (IMO) desirable criterion compliances . It seems to me like a real problem that the absurdity of failing a criterion can depend on whether better criteria require that it be failed. I think this is just cheapness again. Failing mono-raise isn't absurd, because mono-raise is relatively expensive. I think there ought to be a clear distinction between criteria whose violation is absurd no matter what the circumstances, and criteria whose violation is absurd due to other available options. There are very few (named) criteria whose failure I'd call absurd no matter what. Can I take it then that you no longer like CDTT,Random Ballot, which does award a probability pie? Sure. Does your question mean that this really is how you view the difference between CDTT and Mutual Majority, is in terms of the candidates of the winning set sharing a probability pie? Not exactly. No-one has ever suggested MM,Random Ballot as a good method and few have suggested that sometimes the clearly most appropriate winner is not in the MM set (as I have regarding the CDTT set). I think that either isn't relevant or doesn't help your case. The question is about why you view MM's behavior as qualitatively different from CDTT's behavior, when in practice, in a real method, it's exactly the same behavior. If the important thing is how many people suggest that the clearly best winner is not in the MM or CDTT sets, then there doesn't seem to be a good reason to bring up mono-add-plump. The criterion/standard is an end in itself. Not everything is about the strategy game. Higer SU with sincere voting and sparing the method common-sense (at least) difficult -to-counter complaints from the positional-minded are worthwhile accomplisments
Re: [EM] Beatpath GMC compliance a mistaken standard?
Kevin, I can't see what's so highly absurd about failing mono-append. It's basically a limited case of mono-raise, and one that doesn't seem especially more important. Is it absurd to fail mono-raise? The absurdity of failing mono-append is compounded by the cheapness of meeting it. As with mono-add-plump the quasi-intelligent device is given simple and pure new information. Being confused by it is simply unforgivable *stupidity* on the part of the quasi-intelligent device. Regards mono-raise, I would say that failing it is obviously 'positionally absurd' and 'pairwise absurd' but perhaps not 'LNH absurd'. We know that it isn't absurd in the sense that mono-add-plump and mono-append is, because it is failed by a method that has a maximal set of (IMO) desirable criterion compliances . Can I take it then that you no longer like CDTT,Random Ballot, which does award a probability pie? Sure. Does your question mean that this really is how you view the difference between CDTT and Mutual Majority, is in terms of the candidates of the winning set sharing a probability pie? Not exactly. No-one has ever suggested MM,Random Ballot as a good method and few have suggested that sometimes the clearly most appropriate winner is not in the MM set (as I have regarding the CDTT set). The criterion/standard is an end in itself. Not everything is about the strategy game. Higer SU with sincere voting and sparing the method common-sense (at least) difficult -to-counter complaints from the positional-minded are worthwhile accomplisments. This strikes me as an unusual amount of paranoia that the method's results can't be explained to the public's satisfaction unless it's similar to Approval. It isn't just the public. It is myself wearing my common-sense positional hat. And it isn't just Approval, it's 'Approval and/or FPP'. Chris Benham Hi Chris, --- En date de : Jeu 15.1.09, Chris Benham cbenha...@yahoo.com.au a écrit : Kevin, You wrote (12 Jan 2009): Why do we *currently* ever bother to satisfy difficult criteria? What do we mean when we say we value a criterion? Surely not just that we feel it's cheap? When simultaneously a criterion's satisfaction's cost falls below a certain level and its failure reaches a certain level of absurdity/silliness I start to lose sight of the distinction between important for its own sake and very silly not to have because it's so cheap. Mono-add-plump (like mono-append) is way inside that territory. I see. I don't think I value criteria for this sort of reason. If I insist on a criterion like Plurality, it's because I don't think the public will accept the alternative. And these two criteria are relative, so that in order to complain about a violation you have to illustrate a hypothetical scenario in addition to what really occurred. I can't see what's so highly absurd about failing mono-append. It's basically a limited case of mono-raise, and one that doesn't seem especially more important. Is it absurd to fail mono-raise? If you need to identify majorities, then the fact that a ballot shows no preference between Y and Z, is relevant information. In my view a voting method *doesn't* need to specifically identify majorities, so it isn't. (The voting method can and should meet majority-related criteria 'naturally' and obliquely.) But we aren't even talking about voting methods, we're talking about sets. You have basically criticized Schulze(wv) even though it naturally and obliquely satisfies majority-related criteria. But even if the quasi-intelligent device is mistaken in treating them as relevant, then that is a much more understandable and much less serious a blunder than the mono-add-plump failure. Ok. I still don't really see why, or what makes the difference. Imagine the quasi-intelligent device is the captain of a democracy bus that takes on passengers and then decides on its course/destination after polling the passengers. Imagine that as in situation 1 it provisionally decides to go to C, and then as in situation 2 a group of new passengers get on (swelling the total by about 28%) and they are openly polled and they all say we want to go to C, and have nothing else to say and then the captain announces in that case I'll take the bus to B. Would you have confidence that that captain made rational decisions on the most democratic (best representing the passengers' expressed wishes) decisions? I and I think many others would not, and would conclude that the final B decision can only be right if the original C decision was completely ridiculous. Or would you be impressed by the captain's wisdom in being properly swayed by the new passengers' indecision between A and B? However I answer doesn't make any difference, because the question is why this crosses the boundary of clear badness while failures of mono-add-top
[EM] Schulze (Approval-Domination prioritised Margins)
I have an idea for a new defeat-strength measure for the Schulze algorithm (and similar such as Ranked Pairs and River), which I'll call: Approval-Domination prioritised Margins: *Voters rank from the top however many candidates they wish. Interpreting ranking (in any position, or alternatively above at least one other candidate) as approval, candidate A is considered as approval dominating candidate B if A's approval-opposition to B (i.e. A's approval score on ballots that don't approve B) is greater than B's total approval score. All pairwise defeats/victories where the victor approval dominates the loser are considered as stronger than all the others. With that sole modification, we use Margins as the measure of defeat strength.* This aims to meet SMD (and so Plurality and Minimal Defense, criteria failed by regular Margins) and my recently suggested Smith- Comprehensive 3-slot Ratings Winner criterion (failed by Winning Votes). http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html Here is an example where the result differs from regular Margins, Winning Votes and Schwartz//Approval. 44: A 46: BC 07: CA 03: C AB 51-46 = 5 * BC 46-10 = 36 CA 56-44 = 12 Plain Margins would consider B's defeat to be the weakest and elect B, but that is the only one of the three pairwise results where the victor approval-dominates the loser. A's approval opposition to B is 51, higher than B's total approval score of 46. So instead my suggested alternative considers A's defeat (with the next smallest margin) to be the weakest and elects A. Looking at it from the point of view of the Ranked Pairs algorithm (MinMax, Schulze, Ranked Pairs, River are all equivalent with three candidates), the AB result is considered strongest and so locked, followed by the BC result (with the greatest margin) to give the final order ABC. Winning Votes considers C's defeat to be weakest and so elects C. Schwartz//Approval also elects C. Margins election of B is a failure of Minimal Defense. Maybe the B supporters are Burying against A and A is the sincere Condorcet winner. I have a second suggestion for measuring defeat strengths which I think is equivalent to Schwartz//Approval, and that is simply Loser's Approval (interpreting ranking as approval as above, defeats where the loser's total approval score is higher are considered to be weaker than those where the loser's total approval score is lower). Some may see this as more elegant than Schwartz//Approval, and maybe in some more complicated example it can give a different result. Chris Benham Stay connected to the people that matter most with a smarter inbox. Take a look http://au.docs.yahoo.com/mail/smarterinbox Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Beatpath GMC compliance a mistaken standard?
Kevin,
You wrote (10 Jan 2009):
26 AB
25 BA
49 C
Mutual Majority elects {A,B}
Now add 5 A bullet votes:
26 AB
25 BA
49 C
5 A
Now Mutual Majority elects {A,B,C}.
Oops! (I knew that!) Sorry for falsely contradicting you.
Why is mono-add-plump important?
Because as an election method algorithm that fails it
simply can't have any credibility as a quasi-intelligent
device (which is what it is supposed to be) and because
satisfying it should be (and is) very cheap.
I feel that cheapness isn't relevant to whether a criterion is important,
and certainly not to whether failing it is absurd. I save the term
absurd for ideas that are bad regardless of what else is available.
Well I don't. If none of the election criteria were incompatible with each
other, wouldn't we say that nearly all of them are important?
Regarding your first reason: Why is it acceptable to fail mono-add-top
or Participation, but not acceptable to fail mono-add-plump? I guess
that you based this distinction almost entirely on the relative cheapness
of the criteria.
No. With mono-add-top and Participation, the quasi-intelligent device in
reviewing its decision to elect X gets (possibly relevant) information about
other candidates besides X. With mono-add-plump it gets nothing but information
about and purely in favour of X, so it has no excuse at all for changing its
mind
about electing X.
If we view CDTT somehow as an election method, then when it fails
mono-add-plump, the bullet votes for X are not simply strengthening
X, they are also *weakening* some pairwise victory of Y over Z, which X
had relied upon in order to have a majority beatpath to Z.
That just testifies to the absurdity of an algorithm specifically putting
some
special significance on majority beatpaths versus other beatpaths.
You're saying it's absurd, but what is absurd about it?
It's absurd that ballots that plump for X should in any way be considered
relevant
to the strength of the pairwise comparison between two other candidates.
This absurdity only arises from the algorithm specifically using (and relying
on) a
majority threshold.
It would be better, as in less arbitrary, if you simply criticized that
beatpath GMC is
incompatible with ratings summation.
So is Condorcet. I don't think it's particularly arbitrary to value electing
a voted
Shwartz winner. I'm still a bit confused as to why anyone would be interested in
beatpath GMC.
So essentially, Schwartz//Approval is preferable to any method that satisfies
SMD,
Schwartz, and beatpath GMC.
Yes, much preferable to any method that satisfies beatpath GMC period
I don't feel there's an advantage to tending to elect candidates with more
approval, because
in turn this should just make voters approve fewer candidates when they doubt
how the method
will use their vote.
And why is that a negative? I value LNHarm as an absolute guarantee, but in
inherently-
vulnerable-to-Burial Condocet methods, I think it is better if they have a
watch who you rank
because you could help elect them Approval flavour.
From your earlier post:
In the three-candidate case, at least, I think it's a problem to elect a
candidate who isn't in the
CDTT.
Why?
25: AB
26: BC
23: CA
26: C
In this situation 2 election from my demonstration, can you seriously contend
(with a straight face)
that electing C is a problem? Refresh my memory: who first suggested Max.
Approval Opposition
as a way of measuring a candidate's strength?
Chris Benham
Stay connected to the people that matter most with a smarter inbox. Take
a look http://au.docs.yahoo.com/mail/smarterinbox
Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Beatpath GMC compliance a mistaken standard?
Kevin, You wrote (11 Jan 2009): There are reasons for criteria to be important other than how easy they are to satisfy. Otherwise why would we ever bother to satisfy the difficult criteria? Well, if as I said none of the criteria were incompatible with each other then presumably none of the criteria would be difficult. With mono-add-top and Participation, the quasi-intelligent device in reviewing its decision to elect X gets (possibly relevant) information about other candidates besides X. How can it be relevant? X was winning and X is the preferred candidate on the new ballots. You know that Condorcet is incompatible with mono-add-top (and so of course Participation), so if we value compliance with the Condorcet criterion information about candidates ranked below X must sometimes be relevant. But even if the quasi-intelligent device is mistaken in treating them as relevant, then that is a much more understandable and much less serious a blunder than the mono-add-plump failure. It's absurd that ballots that plump for X should in any way be considered relevant to the strength of the pairwise comparison between two other candidates. This absurdity only arises from the algorithm specifically using (and relying on) a majority threshold. We have Mutual Majority and beatpath GMC displaying the same phenomenon. No. I don't accept that 'being tossed out of the favoured (not excluded from winning) set' is exactly the same phenomenon as 'being joined by others in the favoured set'. The latter is obviously far less serious. I don't feel there's an advantage to tending to elect candidates with more approval, because in turn this should just make voters approve fewer candidates when they doubt how the method will use their vote. And why is that a negative? I value LNHarm as an absolute guarantee, but in inherently- vulnerable-to-Burial Condocet methods, I think it is better if they have a watch who you rank because you could help elect them Approval flavour. This is a negative because it suggests that your positional criterion will be self-defeating. How can it possibly be self-defeating? What is there to defeat? From your earlier post: In the three-candidate case, at least, I think it's a problem to elect a candidate who isn't in the CDTT. Why? Because in the three-candidate case this is likely to be a failure of MD or SFC, or close to it. I'm happy to have MD, and I don't care about SFC or close failures of MD. I'm still a bit confused as to why anyone would be interested in beatpath GMC. Well, it's a majority-rule criterion that is compatible with clone independence and monotonicity. Other majority-rule criteria with those same properties will suffice. In the three-candidate case it's also compatible with LNHarm. By adding a vote for your second choice, you can't inadvertently remove your first preference from the CDTT. Well since Condorcet is incompatible with LNHarm, that doesn't explain why Condorcet fans should like it. Also I think this is mainly just putting a positive spin on gross unfairness to truncators and the related silly random-fill incentive. 25: AB 26: BC 23: CA 26: C 100 ballots (majority threshold = 51) BC 51-27, CA 75-25, AB 48-26. In Schulze(Winning Votes), and I think also in any method that meets beatpath GMC and mono-raise, the 26C truncators can virtually guarantee that C be elected by using the random-fill strategy. That is silly and unfair. Also, by artificially denying the clearly strongest candidate any method that doesn't elect C must be vulnerable to Pushover, certainly much more than those that do elect C. http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023590.html (not that that is a very relevant strategy problem for the methods like WV that have the much easier and safer random-fill strategy for the C(B=C) voters.) Chris Benham Stay connected to the people that matter most with a smarter inbox. Take a look http://au.docs.yahoo.com/mail/smarterinbox Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Beatpath GMC compliance a mistaken standard? (was GMC compliance...)
Marcus, You wrote (8 Jan 2009): Statement #1: Criterion X does not imply criterion Y. Statement #2: Criterion X and criterion Y are incompatible. Statement #1 does not imply statement #2. But in your 29 Dec 2008 mail, you mistakenly assume that statement #1 implies statement #2. No I didn't. That is just your mistaken impression. You proved only that beatpath GMC does not imply mono-add-plump; but then you mistakenly concluded that this means that beatpath GMC and mono-add-plump were incompatible (spectacularly vulnerable to mono-add-plump, spectacular failure of mono-add-plump). No, I only wrote that the beatpath GMC *concept* is vulnerable to Mono-add-Plump. However, the fact, that Schulze(winning votes) satisfies beatpath GMC and mono-add-plump, demonstrates that these two criteria are not incompatible. Yes, that is obvious. I explicitly acknowledged this in my last post. I think that all methods that fail Independence from Irrelevant Ballots are silly and that methods should meet the Majority criterion. The Majority *concept* is vulnerable to Irrelevant Ballots because candidate A can be the only candidate allowed to win by the Majority criterion and then we add a handful of ballots that all plump for nobody and candidate A no longer has a majority. But of course I don't suggest that those two criteria are incompatible. The point of my Dec.29 demonstration was to refute any notion or assumption that all candidates in the CDTT (i.e. those not excluded by Beatpath GMC) must be stronger (i.e. more representative of the voters and so more deserving of victory) than any of the candidates outside the CDTT. This was only the first part of my argument that Beatpath GMC [compliance] is a mistaken standard. What other criterion/standard says that the winner must come from set S, with S being a set that a candidate X can be kicked out of by an influx of new ballots that all plump (bullet-vote) for X? I put it to you that the answer is none, and that that makes Beatpath GMC uniquely weird and suspect. By itself that isn't conclusively damning because it doesn't prove that Beatpath GMC can exclude the strongest candidate. 25: AB 26: BC 23: CA 26: C But I contend that here in my situation 2 election Beatpath GMC does exclude the clearly strongest candidate C. You ignored the last few paragraphs of my last post: .. I don't accept your suggestion that compliance with beatpath GMC is acceptably cheap (let alone free), because it isn't compatible with my recently suggested Smith- Comprehensive 3-slot Ratings Winner criterion, which I value much more. http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023595.html In other words the CDTT set can fail to include the candidate that on overwhelming common-sense (mostly positional) grounds is the strongest candidate (e.g. C in Situation # 2). So given a method that meets what I've been recently calling Strong Minimal Defense (and so Minimal Defense and Plurality) and Schwartz (and so fails LNHarm and meets Majority for Solid Coalitions), I consider the addition of compliance with beatpath GMC a negative if without it the method can meet Smith- Comprehensive 3-slot Ratings Winner (which should be very very easy). Chris Benham Dear Chris Benham, you wrote (29 Dec 2008): I think that compliance with GMC is a mistaken standard in the sense that the best methods should fail it. The GMC concept is spectacularly vulnerable to Mono-add-Plump! [Situation #1] 25: AB 26: BC 23: CA 04: C 78 ballots (majority threshold = 40) BC 51-27, CA 53-25, AB 48-26. All three candidates have a majority beat-path to each other, so GMC says that any of them are allowed to win. [Situation #2] But say we add 22 ballots that plump for C: 25: AB 26: BC 23: CA 26: C 100 ballots (majority threshold = 51) BC 51-49, CA 75-25, AB 48-26. Now B has majority beatpaths to each of the other candidates but neither of them have one back to B, so the GMC says that now the winner must be B. The GMC concept is also naturally vulnerable to Irrelevant Ballots. Suppose we now add 3 new ballots that plump for an extra candidate X. [Situation #3] 25: AB 26: BC 23: CA 26: C 03: X 103 ballots (majority threshold = 52) Now B no longer has a majority-strength beat-path to C, so now GMC says that C (along with B) is allowed to win again. (BTW this whole demonstration also applies to Majority-Defeat Disqualification(MDD) and if we pretend that the C-plumping voters are truncating their sincere preference for B over A then it also applies to Eppley's Truncation Resistance and Ossipoff's SFC and GFSC criteria.) I wrote (29 Dec 2008): Your argumentation is incorrect. Example: In many scientific papers, the Smith set is criticized because the Smith set can contain Pareto-dominated candidates. However, to these criticisms I usually reply that the fact
[EM] Beatpath GMC compliance a mistaken standard? (was GMC compliance...)
Marcus, You wrote (29 Dec,2008): You wrote: All three candidates have a majority beatpath to each other, so GMC says that any of them are allowed to win. No! Beatpath GMC doesn't say that any of them are allowed to win; beatpath GMC only doesn't exclude any of them from winning. I can't see that the distinction between allowed to win and not excluded from winning is anything more than that between the glass is half full and the glass is half empty, so I reject your semantic quibble. Any candidate that a criterion C doesn't exclude from winning is (as far as C is concerned) allowed to win. You didn't demonstrate that the GMC concept is spectacularly vulnerable to mono-add-plump. Well, I think I did. Perhaps you misunderstand my use of the word concept. Beatpath GMC says that the winner must come from a certain set S, but a candidate X can fall out of S if a relatively large number of new ballots are added, all plumping (bullet-voting) for X. Is there any other criterion with that absurd feature? However, the fact, that Schulze(winning votes) satisfies mono-add-plump and always chooses from the CDTT set and isn't vulnerable to irrelevant ballots, shows that these properties are not incompatible. Yes, and I never meant to suggest otherwise. In your previous post you (referring to beatpath GMC as the CDTT criterion) wrote: When Woodall's CDTT criterion is violated, then this means that casting partial individual rankings could needlessly lead to the election of a candidate B who is not a Schwartz candidate; needlessly because Woodall's CDTT criterion is compatible with the Smith criterion, independence of clones, monotonicity, reversal symmetry, Pareto, resolvability, etc.. The Schwartz criterion doesn't imply beatpath GMC, so by a Schwartz candidate you mean a '[presumed] sincere Schwartz candidate' instead of a 'voted Schwartz candidate'. I don't accept that this stated aim is necessarily so desirable partly because it isn't the case that (assuming sincere voting and no strategic nominations) a Schwartz candidate is the one that is mostly likely to be the SU winner (as evidenced by my suggested Comprehensive 3-slot Ratings Winner criterion's incompatibility with Condorcet). Secondly I don't accept your suggestion that compliance with beatpath GMC is acceptably cheap (let alone free) because it isn't compatible with recently suggested Smith- Comprehensive 3-slot Ratings Winner criterion, which I value much more. In other words the CDTT set can fail to include the candidate that on overwhelming common-sense (mostly positional) grounds is the strongest candidate (e.g. C in Situation # 2). So given a method that meets what I've been recently calling Strong Minimal Defense (and so Minimal Defense and Plurality) and Schwartz (and so fails LNHarm and meets Majority for Solid Coalitions), I consider the addition of compliance with beatpath GMC a negative if without it the method can meet Smith- Comprehensive 3-slot Ratings Winner (which should be very very easy). Chris Benham Dear Chris Benham, you wrote (29 Dec 2008): The Generalised Majority Criterion says in effect that the winner must come from Woodall's CDTT set, and is defined by Markus Schulze thus (October 1997): Definition (Generalized Majority Criterion): X Y means, that a majority of the voters prefers X to Y. There is a majority beat-path from X to Y, means, that X Y or there is a set of candidates C[1], ..., C[n] with X C[1] ... C[n] Y. A method meets the Generalized Majority Criterion (GMC) if and only if: If there is a majority beat-path from A to B, but no majority beat-path from B to A, then B must not be elected. With full strict ranking this implies Smith, and obviously Candidates permitted to win by GMC (i.e.CDTT), Random Candidate is much better than plain Random Candidate. Nonetheless I think that compliance with GMC is a mistaken standard in the sense that the best methods should fail it. The GMC concept is spectacularly vulnerable to Mono-add-Plump! [Situation #1] 25: AB 26: BC 23: CA 04: C 78 ballots (majority threshold = 40) BC 51-27, CA 53-25, AB 48-26. All three candidates have a majority beat-path to each other, so GMC says that any of them are allowed to win. [Situation #2] But say we add 22 ballots that plump for C: 25: AB 26: BC 23: CA 26: C 100 ballots (majority threshold = 51) BC 51-49, CA 75-25, AB 48-26. Now B has majority beatpaths to each of the other candidates but neither of them have one back to B, so the GMC says that now the winner must be B. The GMC concept is also naturally vulnerable to Irrelevant Ballots. Suppose we now add 3 new ballots that plump for an extra candidate X. [Situation #3] 25: AB 26: BC 23: CA 26: C 03: X 103 ballots (majority threshold = 52) Now B no longer has a majority-strength beat-path to C, so now GMC says that C (along with B) is allowed to win again. (BTW this whole demonstration
[EM] CDTT criterion compliance desirable?
Marcus, You wrote (25 Dec. 2008): Dear Chris Benham, you wrote (25 Dec 2008): I had already proposed this criterion in 1997. Why then do you list it as Woodall's CDTT criterion instead of your own Generalised Majority Criterion? Did, as far as you know, Woodall ever actually proposethe CDTT criterion as something that is desirable for methods to meet (instead of just defining the CDTT set)? Woodall's main aims are to describe and to investigate the different election methods. Compared to the participants of this mailing list, Woodall is very reluctant to say that some election method was good/bad or that some property was desirable/undesirable. That is true, but nonetheless the short answer to my second question is 'no'. To quote Douglas Woodall (with his permission) from a recent email (19 Dec 2008): I defined the CDTT set as a means towards constructing election methods with certain mathematical properties. My memory for such things is not good, and I am open to correction, but as far as I recall I never suggested that for the winner to belong to the CDTT was particularly desirable, and I never suggested this as a criterion. So although calling it Woodall's CDTT criterion is an understandable shorthand, it is somewhat misleading. So can we agree that there isn't really such a thing as Woodall's CDTT criterion and what you have given that label to is your own Generalised Majority Criterion (GMC) that is equivalent to the winner must come from the defined-by-Woodall CDTT set? I'm sorry if this seems excessively nitpicking, and I'm not suggesting you intended to mislead with your understandable shorthand. In my soon-to-follow next post I will explain why I think the GMC is a mistaken standard. Chris Benham Stay connected to the people that matter most with a smarter inbox. Take a look http://au.docs.yahoo.com/mail/smarterinbox Election-Methods mailing list - see http://electorama.com/em for list info
[EM] GMC compliance a mistaken standard? (was CDTT criterion...)
The Generalised Majority Criterion says in effect that the winner must come from Woodall's CDTT set, and is defined by Marcus Schulze thus (October 1997): Definition (Generalized Majority Criterion): X Y means, that a majority of the voters prefers X to Y. There is a majority beat-path from X to Y, means, that X Y or there is a set of candidates C[1], ..., C[n] with X C[1] ... C[n] Y. A method meets the Generalized Majority Criterion (GMC) if and only if: If there is a majority beat-path from A to B, but no majority beat-path from B to A, then B must not be elected. With full strict ranking this implies Smith, and obviously Candidates permitted to win by GMC (i.e.CDTT), Random Candidate is much better than plain Random Candidate. Nonetheless I think that compliance with GMC is a mistaken standard in the sense that the best methods should fail it. The GMC concept is spectacularly vulnerable to Mono-add-Plump! 25: AB 26: BC 23: CA 04: C 78 ballots (majority threshold = 40) BC 51-27, CA 53-25, AB 48-26. All three candidates have a majority beat-path to each other, so GMC says that any of them are allowed to win. But say we add 22 ballots that plump for C: 25: AB 26: BC 23: CA 26: C 100 ballots (majority threshold = 51) BC 51-27, CA 75-25, AB 48-26. Now B has majority beatpaths to each of the other candidates but neither of them have one back to B, so the GMC says that now the winner must be B. The GMC concept is also naturally vulnerable to Irrelevant Ballots. Suppose we now add 3 new ballots that plump for an extra candidate X. 25: AB 26: BC 23: CA 26: C 03: X 103 ballots (majority threshold = 52) Now B no longer has a majority-strength beat-path to C, so now GMC says that C (along with B) is allowed to win again. (BTW this whole demonstration also applies to Majority-Defeat Disqualification(MDD) and if we pretend that the C-plumping voters are trucating their sincere preference for B over A then it also applies to Eppley's Truncation Resistance and Ossipoff's SFC and GFSC criteria.) If the method uses 3-slot ratings ballots and we assume that the voted 3-slot ratings are sincere, then the GMC can bar the plainly highest SU candidate from winning as evidenced by its incompatibility with my recently suggested Smith-Comprehensive 3-slot Ratings Winner criterion: *If no voter expresses more than three preference-levels and the ballot rules allow the expression of 3 preference-levels when there are 3 (or more) candidates, then (interpreting candidates that are voted above one or more candidates and below none as top-rated, those voted above one or more candidates but below all the top-rated candidates as middle-rated and those not voted above any other candidate and below at least one other candidate as bottom-rated, and interpreting above- bottom rating as approval) it must not be possible for candidate X to win if there is some candidate Y which has a beat-path to X and simultaneously higher Top-Ratings and Approval scores and a lower Maximum Approval-Opposition score.* http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023548.html 25: AB 26: BC 23: CA 26: C TR scores: C49, B26, A25 App. scores: C75, B51, A48 MAO scores: C25, B49,A52 That criterion says that C must win here. GMC says only B can win. Frankly I think any method needs a much better excuse than any that Winning Votes can offer for not electing C here. As I discuss in another recent post, any method that doesn't elect C here must be vulnerable to Push-over. So another reason not to be in love with GMC is that it is incompatible with Pushover Invulnerability. http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-December/023543.html As I hope some may have guessed from the spectacular failure of Mono-add-Plump, the GMC concept is grossly unfair to truncators. And Winning Votes (as a GMC complying method) is unfair to truncators. Say the 26C we're just here to elect C and don't care about any other candidate voters use a random-fill strategy, each tossing a fair coin to decide between voting CB or CA; then even if as few as 4 of them vote CA they will elect C. Their chance making C the decisive winner is 99.9956% (according to an online calculator http://stattrek.com/Tables/Binomial.aspx ). I have some sympathy with the idea of giving up something so as to counter order-reversing buriers, but not with the idea that electing a CW is obviously so wonderful that when there is no voted CW we must guess that there is a sincere CW and if we can infer that that can only (assuming no voters are order-reversing) be X then we must elect X. Chris Benham Stay connected to the people that matter most with a smarter inbox. Take a look http://au.docs.yahoo.com/mail/smarterinbox Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Why I think IRV isn't a serious alternative KD
Kristofer, Woodall's DAC and DSC and Bucklin and Woodall's similar QLTD all meet mono-raise and Mutual Majority (aka Majority for Solid Coalitions). DSC meets LNHarm and the rest meet LNHelp. Chris Benham Kristofer Munsterhjelm wrote (Sun.Dec.21): snip In any case, it may be possible to have one of the LNHs and be monotonic and have mutual majority. I'm not sure, but perhaps (doesn't one of DAC or DSC do this?). If so, it would be possible to see (at least) whether people strategize in the direction of early truncation by looking at methods that fail LNHarm but pass LNHelp; that is, Bucklin. snip Stay connected to the people that matter most with a smarter inbox. Take a look http://au.docs.yahoo.com/mail/smarterinbox Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Push-over Invulnerability criterion
Part of my demonstration of many methods' failure of the Unmanipulable Majority criterion has inspired me to suggest another strategy criterion: Push-over Invulnerability: *It must not be possible to change the winner from candidate X to candidate Y by altering some ballots (that vote Y above both candidates X and Z) by raising Z above Y without changing their relative rankings among other (besides X and Z) candidates.* I might later suggest a more elegant re-wording, and/or suggest a simplified approximation that is easier to test for. 25: AB 26: BC 23: CA 26: C BC 51-49, CA 75-25, AB 48-26 Schulze/RP/MM/River (WV) and Approval-Weighted Pairwise and DMC and MinMax(PO) and MAMPO and IRV elect B. Now say 4 of the 26C change to AC (trying a Push-over strategy): 25: AB 04: AC 26: BC 23: CA 22: C BC 51-49, CA 71-29, AB 52-26 Now Schulze/RP/MM/River (WV) and AWP and DMC and MinMax(PO) and MAMPO and IRV all elect C. For a long time I thought that only non-monotonic methods like IRV and Raynaud (that fail mono-raise) were vulnerable to Push-over, so therefore there was no need for a separate Push-over Invulnerability criterion. But now we see that the Schulze, Ranked Pairs, MinMax, River algorithms (all equivalent with 3 candidates) using Winning Votes are all vulnerable to Push-over (as my suggested criterion defines it). Now I know that Winning Votes' failure can be seen as functionally really a failure of Later-no-help, because those C-supporting strategists could more safely achieve the same end just by changing their votes from C to CA instead of from C to AC. But that is hardly a bragging point for WV. I think this Pushover criterion can be seen as a kind of monotonicity criterion, in the sense that all else being equal methods that meet it must be in some way more monotonic than those that don't. I have shown that WV fails Pushover Invulnerability. I strongly suspect (but not at present up to proving) that both Margins and Schwartz//Approval (ranking) meet it. Can anyone please give an example (or examples) that show that either or both of Margins and S//A(r) fail my suggested Push-over Invulnerability criterion? Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Why I Prefer IRV to Condorcet
Kristofer, You wrote (Sun.Nov.23): Regarding number two, simple Condorcet methods exist. Borda-elimination (Nanson or Raynaud) is Condorcet. Minmax is quite simple, and everybody who's dealt with sports knows Copeland (with Minmax tiebreaks). I'll partially grant this, though, since the good methods are complex, but I'll ask whether you think MAM (Ranked Pairs(wv)) is too complex. In MAM, you take all the pairwise contests, sort by strength, and affirm down the list unless you would contradict an earlier affirmed contest. This method is cloneproof, monotonic, etc... Raynaud isn't Borda-elimination. It is Pairwise Elimination, i.e. eliminate the loser of the most decisive or strongest pairwise result (by one measure or another) until one candidate remains. You may have instead meant to write Baldwin,though some sources just talk about 2 different versions of Nanson. Simpler and much better than any of those methods are Condorcet//Approval and Smith//Approval and Schwartz//Approval ,in each case interpreting ranking as approval and so not allowing ranking among unapproved candidates. Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion (Kristofer)
Kristofer Munsterhjelm wrote (Sat.Nov.29): -snip- I don't know of any method that meets the MDQBR you refer to that isn't completely invulnerable to Burial (do you?), so I don't see how that criterion is presently useful. That's odd, because the example I gave in a reply to Juho was yours. http://listas.apesol.org/pipermail/election-methods-electorama.com/2006-December/019097.html Note that the method of that post (which I've been referring to as first preference Copeland) ... -snip- Kristofer, Yes,sorry, that was a not-well-considered posting of mine that I'd forgotten. That method, the basic version of which was introduced by Forest Simmons as Clone-proofed Copeland, doesn't meet Mutual Dominant Quarter Burial Resistance (MDQBR). 26: AB 25: CA 02: CB 25: BA 22: BC AB 51-49, AC 51-49, BC 73-27. FPs: A26, B47, C27. A is the CW and wins with the penalty score of total FPs of candidates pairwise beaten by of zero. With over a quarter of the FPs A is a mutual dominant quarter candidate. Say two of the 25 BA change to BC: 26: AB 25: CA 02: CB 23: BA 24: BC AB 51-49, CA 51-49, BC 73-27 Now the penalty scores are A27, B26, C47. The Burial has worked, the new winner is B. Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] IRV's Squeeze Feature
Forest, You wrote, setting up your attack on IRV: Suppose that the voters are distributed uniformly on a disc with center C, and that they are voting to choose from among several locations for a community center. (a) That is quite a big suppose, and (b) I agree that IRV would not be among the best methods to use to vote to choose the location of a community centre. The center C of any distribution of voters with central symmetry through C will be a Universal Condorcet Option for that distribution. Yes, that is almost a tautology (and to the extent that it isn't it seems to be just a semantic point). And what justification for winning does the IRV winner have? I agree that if we suddenly have unfettered access to all the voters' sincere pairwise preferences and that each voter's different pairwise preferences are all at least approximately as strong as each other, then yes electing the Condorcet winner is nicer and philosophically more justified than electing the IRV winner. However the IRV winner could have as its justification simply the criterion compliances of the IRV method. You, as the election-method salesman, could say to the polity/voters 'customer': This Condorcet method is definitely best for choosing the most central community centre with sincere voting. I recommend it. but they could reply: Does it meet Burial Invulnerability and Later-no-Harm and Later-no-Help as well as Mutual Dominant Third and Mutual Majority and Condorcet Loser and Woodall's Plurality criterion and Clone Independence? To which you must reply No, and then the 'customer' says Then which is the best method that does?, to which you reply IRV and make the sale. IRV has some more-or-less unique problems but they are the unavoidable price of a unique set of strengths, so I don't consider it justified to focus on its problems in isolation. Often this is done, comparing (sometimes implicitly) IRV with the best features of several other methods. But as you know, I am also supportively interested in Condorcet methods and also Favourite Betrayal complying methods such as 3-slot SDC,TR. Chris Benham Forest Simmons wrote (Fri. Dec.5): Suppose that the voters are distributed uniformly on a disc with center C, and that they are voting to choose from among several locations for a community center. Then no matter how many locations on the ballot, if the voters rank them from nearest to furthest, the location nearest to C will be the Condorcet Option. Therefore, if C itself is one of the options, it will be the Condorcet Option no matter what the other options are. So C is more than just a regular run of the mill Condorcet Option, it is a kind of Universal Condorcet Option for this distribution of voters. The center C of any distribution of voters with central symmetry through C will be a Universal Condorcet Option for that distribution. But no matter how peaked that distribution might be (even like the roof of a Japanese pagoda) the center C is not immune from the old IRV squeeze play. If the good and bad cop team gangs up on C, one on each side, they can reduce C's first choice region to a narrow band perpendicular to the line connecting the two team mates, thus forcing C out in the first round of the runoff. If the team mates are not perfectly coordinated, then instead of a narrow band, C's first choice region becomes a long narrow pie piece shaped wedge, roughly perpendicular to the line determined by the two team mates. This squeeze play can be used against any candidate no matter the shape of the distribution, symmetric or not. But my point is that even in a sharply peaked unimodal symetrical distribution, the center C, which is the Universal Condorcet Option, can easily be squeezed out under IRV. And what justification for winning does the IRV winner have? Merely that it was the closer of the two team mates to the ideal location C. Now leaving the concrete setting of voting for a physical location for a community center, and getting back to a more abstract political issue space: It doesn't really matter if the good cop and bad cop are really even anywhere near to opposite sides of a targeted candidate (say a strong third party challenger) as long as they can make it appear that way. The two corporate parties are very good at this good cop / bad cop game, especially since the major media manipulators of public opinion are completely beholden to the giant corporations. Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion
Kristofer, You wrote addressing me: You have some examples showing that RP/Schulze/etc fail the criterion. By my lazy etc. I just meant 'and the other Condorcet methods that are all equivalent to MinMax when there are just 3 candidates and Smith//Minmax when there are not more than 3 candidates in the Smith set'. Do they show that Condorcet and UM is incompatible? Or have they just been constructed on basis of some Condorcet methods, with differing methods for each? My intention was to show that all the methods that take account of more than one possible voter preference-level (i.e. not Approval or FPP) (and are well-known and/or advocated by anyone on EM) are vulnerable to UM except SMD,TP. I think I remember that you said Condorcet implies some vulnerability to burial. Is that sufficient to make it fail UM? Probably yes, but I haven't tried to prove as much. Returning to this demonstration: 93: A 09: BA 78: B 14: CB 02: CA 04: C 200 ballots BA 101-95, BC 87-20, AC 102-20. All Condorcet methods, plus MDD,X and MAMPO and ICA elect B. B has a majority-strength pairwise win against A, but say 82 of the 93A change to AC thus: 82: AC 11: A 09: BA 78: B 14: CB 02: CA 04: C BA 101-95, CB 102-87, AC 102-20 Approvals: A104, B101, C102 TR scores: A93, B87, C 20 Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using WV or Margins elect A. So all those methods fail the UM criterion. Working in exactly the same way as ICA (because no ballots have voted more than one candidate top), this also applies to Condorcet//Approval and Smith//Approval and Schwartz//Approval. So those methods also fail UM. I did a bit of calculation and it seems my FPC (first preference Copeland) variant elects B here, as should plain FPC. Since it's nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure whether that can be fixed at all. My impression is/was that in 3-candidates-in-a-cycle examples that method behaves just like IRV. The demonstration that I gave of IRV failing UM certainly also applies to it. Chris Benham Kristofer Munsterhjelm wrote (Thurs.Dec.4): Chris Benham wrote: Regarding my proposed Unmanipulable Majority criterion: *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make Bthe winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.* To have any point a criterion must be met by some method. It is met by my recently proposed SMD,TR method, which I introduced as 3-slot SMD,FPP(w): *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* [snip examples of methods failing the criterion] You have some examples showing that RP/Schulze/etc fail the criterion. Do they show that Condorcet and UM is incompatible? Or have they just been constructed on basis of some Condorcet methods, with differing methods for each? I think I remember that you said Condorcet implies some vulnerability to burial. Is that sufficient to make it fail UM? I wouldn't be surprised if it is, seeing that you have examples for a very broad range of election methods. 93: A 09: BA 78: B 14: CB 02: CA 04: C 200 ballots BA 101-95, BC 87-20, AC 102-20. All Condorcet methods, plus MDD,X and MAMPO and ICA elect B. B has a majority-strength pairwise win against A, but say 82 of the 93A change to AC thus: 82: AC 11: A 09: BA 78: B 14: CB 02: CA 04: C BA 101-95, CB 102-87, AC 102-20 Approvals: A104, B101, C102 TR scores: A93, B87, C 20 Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using WV or Margins elect A. So all those methods fail the UM criterion. I did a bit of calculation and it seems my FPC (first preference Copeland) variant elects B here, as should plain FPC. Since it's nonmonotonic, it's vulnerable to Pushover, though, and I'm not sure whether that can be fixed at all. Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Why I think IRV isn't a serious alternative
Forest, What nicer distribution can you think of.. Nice (and nicer) is a fuzzy emotional/aesthetic term that I might apply to food, music, people etc. but seems unscientific and out-of-place here (and I'm not sure exactly what it's supposed to mean). I can see that such a distribution is more comfortable for methods that try to elect the centrist candidate. I see IRV as FPP that trades most of its monotonicity criteria (including mono-raise and Participation but not mono-add-top, mono-add-plump or mono-append) to gain Clone-Winner and Majority for Solid Coalitions (and Mutual Dominat Third and Condorcet Loser). It keeps FPP's compliances with Woodall's Plurality criterion, Later-no-Harm, Later-no-Help and Clone-Loser. The representativeness criteria it meets generally allow for a bigger set of allowable winners than say the Smith set, and its monotonity failures mean that it chooses a winner from this set a bit erratically. But I think your use of the term pathology (comparing it to a disease and so something that is self-evidently unacceptable) is biased and out of place. I also think that the argument that IRV makes a good stepping-stone to PR is strong. Truly proportional multi-winner methods meet Droop Proportionality for Solid Coalitions (equivalent in the single-winner case to Majority for Solid Coalitions, aka Mutual Majority.) Single-winner STV's virtues of Later-no-Harm and Clone Independence survive into the multi-winner version (which of course meets Droop Proportionality SC), while for multi-winner methods the Condorcet criterion and Favourite Betrayal are both incompatible with Droop PSC. Also I think Later-no-Harm compliance is more valuable for multi-winner methods than for single-winner methods. Chris Benham Forest Simmons wrote (Sat. Nov.29): From: Chris Benham Forest, Given IRV's compliance with the representativeness criteria Mutual Dominant Third, Majority for Solid Coalitions, Condorcet Loser and? Plurality; why should the bad look of its erratic behaviour be sufficient to condemn IRV in spite of these and other positive criterion compliances such as Later-no-Harm and Burial Invulnerability? A picture is worth a thousand words. It shows the actual behavior, including the extent of the pathology. in the best of all possible worlds, namely normally distributed voting populations in no more than two dimensional issue space. CB: Why does that situation you refer to qualify as the best of all possible worlds ? Three points determine a plane, so we cannot expect a lower dimension than two. What nicer distribution can you think of. than normal? But any distribution whose density only depends on distance from the center of the distribution would give exactly the same results for any Condorcet method, without making the IRV results any nicer. Forest Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion (newly amended version)
Regarding my proposed Unmanipulable Majority criterion: *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.* To have any point a criterion must be met by some method. It is met by my recently proposed SMD,TR method, which I introduced as 3-slot SMD,FPP(w): *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* Referring to the UM criterion: (a) if candidate A has a higher TR score than B then the BA strategists can only make B win by causing A to be disqualified. But in this method it isn't possible to vote x above y without approving x, so we know that just on the AB ballots A has majority approval. It isn't possible for a majority-approved candidate to be disqualified, and the strategists can't cause A's approval to fall below majority-strength. And the criterion specifies that none of the BA voters who don't top-rate B can raise their rating of B to increase B's TR score. (b) if on the other hand B has a higher TR score than A but B is disqualified there is nothing the BA strategists can do to undisqualify B. So SMD,TR meets the UM criterion. 93: A 09: BA 78: B 14: CB 02: CA 04: C 200 ballots BA 101-95, BC 87-20, AC 102-20. All Condorcet methods, plus MDD,X and MAMPO and ICA elect B. B has a majority-strength pairwise win against A, but say 82 of the 93A change to AC thus: 82: AC 11: A 09: BA 78: B 14: CB 02: CA 04: C BA 101-95, CB 102-87, AC 102-20 Approvals: A104, B101, C102 TR scores: A93, B87, C 20 Now MDD,A and MDD,TR and MAMPO and ICA and Schulze/RP/MinMax etc. using WV or Margins elect A. So all those methods fail the UM criterion. 25: AB 26: BC 23: CA 26: C BC 51-49, CA 75-25, AB 48-26 Schulze/RP/MM/River (WV) and Approval-Weighted Pairwise and DMC and MinMax(PO) and MAMPO and IRV elect B. Now say 4 of the 26C change to AC (trying a Push-over strategy): 25: AB 04: AC 26: BC 23: CA 22: C BC 51-49, CA 71-29, AB 52-26 Now Schulze/RP/MM/River (WV) and AWP and DMC and MinMax(PO) and MAMPO and IRV all elect C. Since B had/has a majority-strength pairwise win against C, all these methods also fail Unmanipulable Majority. If scoring ballots were used and all voters score their most preferred candidate 10 and any second-ranked candidate 5 and unranked candidates zero, then this demonstration also works for IRNR so it also fails. Who knew that such vaunted monotonic methods as WV and MinMax(PO) and MAMPO were vulnerable to Push-over?! 48: AB 01: A 03: BA 48: CB BA 51-49. Bucklin and MCA elect B, but if the 48 AB voters truncate the winner changes to A. So those methods also fail UM. 49: A9, B8, C0 24: B9, A0, C0 27: C9, B8, A0 Here Range/Average Ratings/Score/CR elects B and on more than half the ballots B is voted above A, but if the 49 A9, B8, C0 voters change to A9, B0, C0 the winner changes to A. So this method fails UM. 48: ABCD 44: BADC 04: CBDA 03: DBCA Here Borda elects B and B is voted above A on more than half the ballots, but if the 48 ABCD ballots are changed to ACDB the Borda winner changes to A, so Borda fails UM. This Unmanipulable Majority criterion is failed by all well known and currently advocated methods, except 3-slot SMD,TR! Given its other criterion compliances and simplicity, that is my favourite 3-slot s-w method and my favourite Favourite Betrayal complying method. Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion definition amended
I propose to amend my suggested Unmanipulable Majority criterion by simply adding a phrase beginning with without.. so that it now reads: *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A without raising their ranking or rating of B.* (Later I might rephrase it just to make it more succinct and polished). The effect of the alteration is to preclude Compromise strategy. When I first suggested the original version I knew that many methods fail it due to Burial and/or Push-over, but I mistakenly thought that my recent 3-slot method suggestion (defined below) meets it. *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their maximum approval-opposition (MAO) score. (X's MAO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* My preferred name for that method is now Strong Minimal Defense, Top Ratings (SMD,TR). 45: A 03: AB 47: BA 02: XB 03: YA Approvals: A98, B52, Y3, X2 Max. AO: A2, B48, Y95, X95 Top Ratings: A48, B47, Y3, X2. X and Y are disqualified, and A wins. A is voted above B on more than half the ballots, but if all the ballots on which B is voted above A are altered so that they all plump for B (top-rate B and approve no other candidates) then B wins. 45: A 03: AB 49: B 03: YA Approvals: A51, B52, Y3, X0 Max. AO: A49, B48, Y52, X52 Top Ratings: A48, B49, Y3, X0 As before only X and Y are disqualified, but now B has the highest Top Ratings score. I will soon post more on the subject of which methods meet or fail the (newly amended) Unmanipulable Majority criterion. Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion
Kristofer, ...your Dominant Mutual Quarter Burial Resistance property. I don't remember reading or hearing about anything like that with Quarter in the title anywhere except in your EM posts. A few years ago James Green-Armytage coined the Mutual Dominant Third criterion but never promoted it. I took it up, but sometimes mistakenly reversed the order of the first two words. I now think the original order is better, because MDT is analogous with the better-known older Mutual Majority criterion. I do remember suggesting what is in effect MDT Burial Resistance, because there is an ok method that meets it while failing Burial Invulnerability: namely Smith,IRV. I don't know of any method that meets the MDQBR you refer to that isn't completely in invulnerable to Burial (do you?), so I don't see how that criterion is presently useful. In response to my question is Unmanipulative Majority desirable? you wrote: In isolation (not affecting anything else), sure. It's desirable because it limits the burying tricks that can be done. I'm glad you think so. The mention of pushover strategy there would mean that the method would have to have some degree of monotonicity, I assume. Yes. If AX voters can cause A to win by rearranging their ballots, then that would be a form of constructive burial. If, for instance, some subset of the voters who place X fifth can keep X from winning by rearranging their first-to-fourth preferences, then that would be destructive burial. If those voters are sincere in ranking X fifth, i.e they sincerely prefer all the candidates they rank above X to X; then I can't see that that qualifies as Burial strategy at all. Normally the strategy you refer to would qualify as some form of Compromise strategy. (Do you have an example that doesn't?) Chris Benham Kristofer Munsterhjelm wrote (Fri.Nov.28) wrote: Chris Benham wrote: Kristofer, Thanks for at least responding. ...I won't say anything about the desirability because I don't know what it implies;.. Only judging criteria by how they fit in with other criteria is obviously circular. That's true. If we're going to judge criteria by how they fit in with other criteria, we should have an idea of how relatively desirable they are. It may also be the case that it the tradeoff would be too great, by reasoning similar to what I gave in the reply to Juho about your Dominant Mutual Quarter Burial Resistance property. But if we consider this in more detail, we don't really know whether such tradeoffs are too great for, for instance, cloneproof criteria (though I think they are not). Do you (or anyone) think that judged in isolation this strategy criterion is desirable? It is true that some desirable/interesting criteria are so restrictive (as you put it) that IMO compliance with them can only be a redeeming feature of a method that isn't one of the best. (I put Participation in that category.) In isolation (not affecting anything else), sure. It's desirable because it limits the burying tricks that can be done. If you're asking whether I think it's more important than being, say, cloneproof, I don't think I can answer at the moment. I haven't thought about the relative desirability of criteria, though I prefer Condorcet methods to be both Smith and cloneproof. Maybe some people would like me to paraphrase this suggested criterion in language that is more EM-typical: 'If candidate A majority-strength pairwise beats candidate B, then it must not be possible for B's supporters (pairwise versus A) to use Burial or Pushover strategy to change the winner from A to B.' The mention of pushover strategy there would mean that the method would have to have some degree of monotonicity, I assume. Destructive burial would be trying to make X not win,... Your destructive burial looks almost synonymous with *monotonicity*. Hm, not necessarily. Without qualifications on the criterion, destructive burial would be constructive burial for *any* candidate, but also more than that. If AX voters can cause A to win by rearranging their ballots, then that would be a form of constructive burial. If, for instance, some subset of the voters who place X fifth can keep X from winning by rearranging their first-to-fourth preferences, then that would be destructive burial. Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Why I think IRV isn't a serious alternative
Forest, Given IRV's compliance with the representativeness criteria Mutual Dominant Third, Majority for Solid Coalitions, Condorcet Loser and Plurality; why should the bad look of its erratic behaviour be sufficient to condemn IRV in spite of these and other positive criterion compliances such as Later-no-Harm and Burial Invulnerability? in the best of all possible worlds, namely normally distributed voting populations in no more than two dimensional issue space. Why does that situation you refer to qualify as the best of all possible worlds ? Chris Benham Forrest Simmons wrote (Wed. Nov.26): Greg, When someone asks for examples of IRV not working well in practice, they are usually protesting against contrived examples of IRV's failures. Sure any method can be made to look ridiculous by some unlikely contrived scenario. I used to sympathize with that point of view until I started playing around with examples that seemed natural to me, and found that IRV's erratic behavior was fairly robust. You could vary the parameters quite a bit without shaking the bad behavior. But I didn't expect anybody but fellow mathematicians to be able to appreciate how generic the pathological behavior was, until ... ... until the advent of the Ka-Ping Lee and B. Olson diagrams, which show graphically the extent of the pathology even in the best of all possible worlds, namely normally distributed voting populations in no more than two dimensional issue space. These diagrams are not based upon contrived examples, but upon benefit-of-a-doubt assumptions. Even Borda looks good in these diagrams because voters are assumed to vote sincerely. Each diagram represents thousands of elections decided by normally distributed sincere voters. I cannot believe that anybody who supports IRV really understands these diagrams. Admittedly, it takes some effort to understand exactly what they represent, and I regret that the accompaning explanations are too abstract for the mathematically naive. They are a subtle way of displaying an immense amount of information. One way to make more concrete sense out of these diagrams is to pretend that each of the candidate dots actually represents a proposed building site, and that the purpose of each simulated election is to choose the site from among these options. Each of the other pixels in the diagram represents (by its color) the outcome the election would have (under the given method) if a normal distribution of voters were centered at that pixel. So each pixel of the diagram represents a different election, but with the same candidates (i.e. proposed construction sites). Different digrams explore the effect of moving the candidates around relative to each other, as well as increasing the number of candidates. With a little practice you can get a good feel for what each diagram represents, and what it says about the method it is pointed at (as a kind of electo-scope). On result is that IRV shows erratic behavior even in those diagrams where every pixel represents an election in which there is a Condorcet candidate. My Best, Forest Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Unmanipulable Majority strategy criterion
I have a suggestion for a new strategy criterion I might call Unmanipulable Majority. *If (assuming there are more than two candidates) the ballot rules don't constrain voters to expressing fewer than three preference-levels, and A wins being voted above B on more than half the ballots, then it must not be possible to make B the winner by altering any of the ballots on which B is voted above A.* Does anyone else think that this is highly desirable? Is it new? Chris Benham Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=otherp2=aup3=tagline Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Why I Prefer IRV to Condorcet
Greg, I generally liked your essay. I rate IRV as the best of the single-winner methods that meet Later-no-Harm, and a good method (and a vast improvement on FPP). But I think you made a couple of technical errors. However, because bullet voting can help and never backfire against one's top choice under Condorcet, expect every campaign with a shot at winning to encourage its supporters to bullet vote. Bullet voting can backfire against one's top choice under Condorcet because Condorcet methods, unlike IRV, fail Later-no-Help. http://groups.yahoo.com/group/election-methods-list/files/wood1996.pdf In this 1996 Douglas Woodall paper, see Election 6 and the accompanying discussion on page 5/6 of the pdf (labelled on the paper as Page 13). Quoting again from your paper: As mentioned, every voting system is theoretically vulnerable to strategic manipulation, and IRV is no exception. However, under IRV, there is no strategy that can increase the likelihood of electing one's first choice beyond the opportunity offered by honest rankings. While there are strategies for increasing the chances of less preferred candidates under IRV, like push-over, they are counter-intuitive. The Push-over strategy is certainly not limited to improving the chance of electing a lower [than first] choice. Say sincere is: 49: A 27: BA 24: CB B is the IRV winner, but if 4-21 (inclusive) of the A voters change to C or C? then the winner changes to A. But as you say the strategy isn't intuitive , and backfires if too many of the A supporters try it. Some IRV opponents claim to like Top-Two Runoff, but that is more vulnerable to Push-over than IRV (because the strategists can support their sincere favourite in the second round). The quite intuitive strategy that IRV is vulnerable to is Compromise, like any other method that meets Majority. But voters' incentive to compromise (vote one's front-runner lesser-evil in first place to reduce the chance of front-runner greater-evil winning) is generally vastly vastly less than it is under FPP. (There are methods that meet both Majority and Favourite Betrayal, and in them compromisers can harmlessly vote their sincere favourites in equal-first place.) But some Condorcet advocates are galled by the Compromise incentive that can exist where there is a sincere CW who is not also a sincere Mutual Dominant Third winner. 49: AB 02: BA 22: B 27: CB On these votes B is the CW, but IRV elects A. If the CB voters change to B then B will be the voted majority favourite, so of course IRV like Condorcet methods and FPP will elect B. Chris Benham Greg wrote (Wed.Nov.19, 2008): I have written up my reasons for preferring IRV over Condorcet methods in an essay, the current draft of which is available here: http://www.gregdennis.com/voting/irv_vs_condorcet.html I welcome any comments you have. Thanks, Greg Make the switch to the world#39;s best email. Get Yahoo!7 Mail! http://au.yahoo.com/y7mail Election-Methods mailing list - see http://electorama.com/em for list info
[EM] New MN court affidavits by those defending non-Monotonic voting methods IRV/STV
Greg wrote (Th.Nov.6): Those documents make a good case. If you rule IRV/STV unconstitutional due to non-monotonicity, you have to be prepared to rule open primaries and top-two primaries unconstitutional as well. Note also that other arguments by the MN Voter's Alliance would, if successful, would render *any* voting method that involves putting marks next to multiple candidates -- IRV, Bucklin, Approval, Condorcet, Range -- by its nature unconstitutional. -snip- That anti-IRV group explicitly say as much: Additional note: There are several other non-traditional voting methods currently being advocated around the country. Among these are Range Voting and Approval Voting. (See the NYU report linked above) While these schemes are better in some ways than IRV, they retain some of the same fatal flaws which make IRV unconstitutional. http://www.mnvoters.org/IRV.htm Chris Benham Find your perfect match today at the new Yahoo!7 Dating. Get Started http://au.dating.yahoo.com/?cid=53151pid=1012 Election-Methods mailing list - see http://electorama.com/em for list info
[EM] In defense of the Electoral College (was Re: Making a Bad Thing Worse)
Kevin Venzke wrote (Fri.Nov.7): Hi, --- En date de : Ven 7.11.08, Markus Schulze markus.schulze at alumni.tu-berlin.de a écrit : Second: It makes it possible that the elections are run by the governments of the individual states and don't have to be run by the central government. I especially agree with this second point, or at least that it has been a good thing that the elections have not been conducted by a single authority. It's possible to imagine a different American history, if the federal government had been in a position to cancel or postpone or manipulate the presidential election. Kevin Venzke Kevin, Why does having elections for national office run by a central authority like a federal electoral commission necessarily mean that the federal government (presumably you refer here to partisan office-holders with a stake in the election outcome) would have the power to cancel or postpone or manipulate the presidential election? Can you please support your point by comparing the US with other First World countries, perhaps just focussing on the last few decades? Chris Benham Find your perfect match today at the new Yahoo!7 Dating. Get Started http://au.dating.yahoo.com/?cid=53151pid=1012 Election-Methods mailing list - see http://electorama.com/em for list info
[EM] New MN court affidavits by those defending non-Monotonic voting methods IRV/STV
Dave, Are you really comfortable supporting and supplying ammunition to a group of avowed FPP supporters in their effort to have IRV declared unconstitutional? Will have any complaint when in future they are trying to do the same thing to some Condorcet method you like and IRV supporters help them on grounds like it fails Later-no-Harm, Later-no-Help, and probably mono-add-top? Chris Benham Dave Ketchum wrote (Fri.Nov.7): Perhaps this could get some useful muscle by adding such as: 9 BA Now we have 34 voting BA. Enough that they can expect to win and may have as strong a preference between these two as might happen anywhere. C and D represent issues many feel strongly about - and can want to assert to encourage action by B, the expected winner. If ONE voter had voted BA rather than DBA, IRV would have declared B the winner. Note that Condorcet would have declared B the winner any time the BA count exceeded the AB count (unless C or D got many more votes). DWK On Fri, 7 Nov 2008 14:05:03 -0700 Kathy Dopp wrote: Dave, I agree with you -that is important too, but the attorneys and judge(s) have their own criteria for judging importance as compared to existing laws. Your example IMO does show unequal treatment of voters, so perhaps I'll include it as one of many ways to show how IRV unequally treats voters and see if the attorneys use it or not. Thanks. Kathy Find your perfect match today at the new Yahoo!7 Dating. Get Started http://au.dating.yahoo.com/?cid=53151pid=1012 Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] In defense of the Electoral College (was Re: Making a Bad Thing Worse)
Steve Eppley wrote (Th. Nov.6): Hi, Greg Nisbet wrote on 10/18/08: -snip- The Electoral College: This is generally regarded as a bad thing. No one really appears to support it except as an adhoc version of asset voting. -snip- I don't believe the EC is generally accepted as a bad thing. (I picked the Subject line above to cite a book by the same name.) Although I may have been the person who came up with the idea for how to get rid of the EC without a constitutional amendment (posted in EM many years ago), I later concluded the EC is better than a national popular vote. -snip- One widespread argument against the EC is that it flouts the commonsense fairness axiom that all votes should be weighted equally. A national popular vote would exacerbate polarization, since candidates could/would focus on voter turnout of their base instead of having to appeal to swing voters in a few close states. I don't see how preventing the supposed evil of exacerbating polarisation anything like justifiies the unfairness evil of weighting votes unequally. And in any case I don't accept the argument. Why wouldn't candidates have incentive to appeal to swing voters *across the whole country*?? Why would anyone go to the trouble of elaborating and proposing a relatively complicated ranked-ballot method that is justified by meeting the Condorcet criterion and Majority for Solid Coalitions and so on, and then turn around and suggest that it is desirable that weighting votes unequally should be maintained, thus ensuring that any voting method cannot meet those criteria or even Majority Favourite or Majority Loser? A national popular vote would exacerbate the candidates' need for campaign money, since they would not be able to focus on the few states that are close. That would make them more beholden to wealthy special interests. A national popular vote would make for a nightmare when recounting a close election. The recounting wouldn't be confined to a few close states. Plenty of other countries directly elect their presidents without any EC, and yet it is the US that has these problems (more severely). I think the counting problems would be less likely with a national popular vote, simply because it is very unlikely to be very close. The scenario that it is very close in some (using the the EC) critical states but not close in the overall popular vote is much more likely than it being very close in both. Chris Benham Search 1000's of available singles in your area at the new Yahoo!7 Dating. Get Started http://au.dating.yahoo.com/?cid=53151pid=1011 Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Re : About Condorcet//Approval
Kevin, I've always thought that the main value of mono-raise is that methods that fail it are vulnerable to Pushover strategy and those that meet it aren't. push-over The strategy of ranking a weak alternative higher than one's preferred alternative, which may be useful in a method that violates monotonicity. http://condorcet.org/emr/defn.shtml But now you are proposing an interpretation of mono-raise (aka monotonicity) that can be met by a method that is clearly vulnerable to Pushover strategy. 25: AB 26: BC 23: CA 26: C What is the value/use of a criterion that does that and moreover can be met by a method that fails to elect C in the above election? The method under discussion that you say meets mono-raise, Definite Majority Choice (Whole), elects B. All candidates are in the top cycle, but by our 3-slot ratings ballot interpretation C has the highest TR score, the highest approval score, and the lowest approval-opposition score. Would you agree then that there is a need for an Invulnerability to Pushover strategy criterion, that is more important than mono-raise? Chris Benham Hi Chris, --- En date de : Jeu 23.10.08, Chris Benham cbenhamau at yahoo.com.au a écrit : Kevin, I think the version of DMC that allows voters to rank among unapproved candidates fails mono-raise, and both versions are vulnerable to Pushover strategy. Would you say that that the plain all ranked are approved version doesn't properly fail mono-raise but instead fails mono-raise-delete? I think it definitely fails the latter. I think it only fails the former if you can't rank all the candidates (for approval purposes). http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-March/019824.html I wrote in March 2007: With the approval cutoffs, DMC (and AWP) come close to failing mono-raise. 31: AB 04: AC 32: BC 33: CA ABCA Approvals: A35, B32, C33. A eliminates (doubly defeats) B, and C wins. (AWP measures defeat-strengths by the number of ballots on the winning side that approve the winner and not the loser, and so says C's defeat is the weakest and so also elects C.) Now change the 4 AC ballots to CA To my mind you aren't allowed to move C over both A and the cutoff at the same time, unless the method for some reason doesn't allow it any other way (such as if this is the bottom of the ballot and you can't approve all candidates). Kevin Venzke I misstated something: --- En date de : Dim 26.10.08, Kevin Venzke stepjak at yahoo.fr a écrit : Now change the 4 AC ballots to CA To my mind you aren't allowed to move C over both A and the cutoff at the same time, unless the method for some reason doesn't allow it any other way (such as if this is the bottom of the ballot and you can't approve all candidates). You can move C over both at the same time, but you can't, at this same time, move A and the cutoff relative to each other, according to my opinion. Kevin Venzke Search 1000's of available singles in your area at the new Yahoo!7 Dating. Get Started http://au.dating.yahoo.com/?cid=53151pid=1011 Election-Methods mailing list - see http://electorama.com/em for list info
[EM] About Condorcet//Approval
Kevin, I think the version of DMC that allows voters to rank among unapproved candidates fails mono-raise, and both versions are vulnerable to Pushover strategy. Would you say that that the plain all ranked are approved version doesn't properly fail mono-raise but instead fails mono-raise-delete? http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-March/019824.html I wrote in March 2007: With the approval cutoffs, DMC (and AWP) come close to failing mono-raise. 31: AB 04: AC 32: BC 33: CA ABCA Approvals: A35, B32, C33. A eliminates (doubly defeats) B, and C wins. (AWP measures defeat-strengths by the number of ballots on the winning side that approve the winner and not the loser, and so says C's defeat is the weakest and so also elects C.) Now change the 4 AC ballots to CA 31: AB 32: BC 37: CA (4 were AC) ABCA Approvals: C37, B32, A31 Now C doubly defeats A, and B wins. (AWP also elects B) http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-October/023017.html Chris Benham Kevin Venzke wrote (Mon.Oct.20): Hi Kristofer, --- En date de : Lun 20.10.08, Kristofer Munsterhjelm km-elmet at broadpark.no a écrit : You could also have the approval version of Smith,IRV. Call it Condorcet,Approval. I think it's Smith (so it would be Smith,Approval), but I'm not sure. The method is this: Drop candidates, starting with the Approval loser and moving upwards, until there's a CW. Then that one is the winner. This method has been invented from scratch a few times; most recently it was called Definite Majority Choice. I don't think it can be described using double-slash or comma notation... For instance Smith//FPP would mean that you eliminate all non-Smith candidates and elect the FPP winner pretending that the eliminated candidates never existed. Whereas Smith,FPP would mean that you elect that Smith candidate who had the most first preferences to start with. When Condorcet is the first or Approval is the second component, it's not likely to make a difference which punctuation is used. Is Condorcet,Approval (Smith,Approval?) nonmonotonic? If not, and it is Smith, then you have a simple Smith-compliant Condorcet/approval method. It satisfies Smith and monotonicity. Kevin Venzke Send instant messages to your online friends http://au.messenger.yahoo.com Election-Methods mailing list - see http://electorama.com/em for list info
[EM] About Condorcet//Approval
Kristofer Munsterhjelm wrote (Sat.Oct.18): Because Smith is more complex to explain, my current favorite election method is Condorcet//Approval. We don't need complex algorithms to find a winner. You could also have the approval version of Smith,IRV. Call it Condorcet,Approval. I think it's Smith (so it would be Smith,Approval), but I'm not sure. The method is this: Drop candidates, starting with the Approval loser and moving upwards, until there's a CW. Then that one is the winner. Kristofer, The method you describe isn't Smith,Approval (which is the same thing as Smith//Approval). Smith,Approval elects the member of the Smith set highest-ordered by Approval on the original ballots, Smith//Approval first eliminates (drops from the ballots) all non-members of the Smith set and applies Approval to the remaining candidates. Since approval is treated as 'absolute' it doesn't make a difference like it does between Smith,IRV and Smith//IRV. The method you describe has IRV-like mono-raise failure and Pushover strategy vulnerability. 31: AB 32: BC 31: CA 06: C All ranked candidates are approved, and all candidates are in the Smith set. AB 62-32, BC 63-31, CA 69-31. Approval scores: A62, B63, C69. A is eliminated and B wins, but if 2 of the 6 C votes change to A then C wins. 31: AB 32: BC 31: CA 04: C 02: A The Approval winner C is the clearly strongest candidate (the most first preferences and the most second preferences) in both cases. These methods would obviously need approval cutoff ballots (unless you go with the MDDA assumption, that the approval cutoff is where the voter truncates, but I don't think that would be a good idea here). Here I agree with Kevin Venzke. Allowing voters to rank among candidates they don't approve just makes the method more vulnerable to Burial strategy and makes the proposal much more complex. Chris Benham Send instant messages to your online friends http://au.messenger.yahoo.com Election-Methods mailing list - see http://electorama.com/em for list info
[EM] 3-slot SMD,ER-FPP(w)
--- En date de : Dim 19.10.08, Chris Benham cbenhamau at yahoo.com.au a écrit : I have an idea for a new 3-slot voting method: *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their approval-opposition (AO) score. (X's AO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* Kevin Venzke wrote (Mon.Oct.20): Interesting method, but I'm concerned that rating a candidate in the middle can disqualify other candidates, but can't help this candidate win, except by preventing him from being disqualified himself. It seems like a burial risk. With two major factions supporting A and B, and a third candidate C, if A faction buries B under C, I believe A will often win. Does B faction have a defensive strategy that isn't the same as the offensive strategy? I don't think they do. Actually, this method isn't that far from MDD,FPP. CB: Except that method fails Irrelevant Ballots and I think meets LNHarm. This clearly meets Favourite Betrayal, Participation, mono-raise, mono-append, 3-slot Majority for Solid Coalitions, Strong Minimal Denfense (and so Minimal Defense and Woodall's Plurality criterion), Independence of Irrelevant Ballots. I don't think it satisfies Participation, because your favorite candidate could be winning, and when your vote is added, you add sufficient approval to your compromise choice that they are no longer disqualified, and are able to win instead of your favorite. CB: Oops!.. you are right. It fails Participation and even Mono-add-Top. 8: C 3: F 2: XF 2: YF 2: ZF F wins after all other candidates are disqualified, but if 2 FC ballots are added C wins in exactly the way you describe. It looks like the Strong Minimal Defense mechanism is incompatible with Participation, so I was also wrong in suggesting that my recent Range-Approval hybrid method suggestion meets Participation. I still like this 3-slot SMD,FPP(w) method however and am confident the other criterion compliances I claimed for it hold up. Chris Benham Send instant messages to your online friends http://au.messenger.yahoo.com Election-Methods mailing list - see http://electorama.com/em for list info
[EM] 3-slot SMD,ER-FPP(w)
I have an idea for a new 3-slot voting method: *Voters fill out 3-slot ratings ballots, default rating is bottom-most (indicating least preferred and not approved). Interpreting top and middle rating as approval, disqualify all candidates with an approval score lower than their approval-opposition (AO) score. (X's AO score is the approval score of the most approved candidate on ballots that don't approve X). Elect the undisqualified candidate with the highest top-ratings score.* This clearly meets Favourite Betrayal, Participation, mono-raise, mono-append, 3-slot Majority for Solid Coalitions, Strong Minimal Denfense (and so Minimal Defense and Woodall's Plurality criterion), Independence of Irrelevant Ballots. This 3-slot Strong Minimal Defense, Equal-Ranking First-Preference Plurality (Whole) method is my new clear favourite 3-slot single-winner method. One small technical disadvantage it has compared to Majority Choice Approval (MCA) and ER-Bucklin(Whole) and maybe Kevin Venzke's ICA method is that it fails what I've been calling Possible Approval Winner (PAW). 35: A 10: A=B 30: BC 25: C Approval scores: A45, B40, C55 Approval Opp.: A55, B35, C45 Top-ratings score: A45, B40, C25. C's approval opposition to A is 55, higher than A's approval score of 45, so A is disqualified. The undisqualified candidate with the highest top-ratings score is B, so B wins. But if we pretend that on each ballot there is an invisible approval threshold that makes some distinction among the candidates but not among those with the same rank, then B cannot have an approval score as high a A's. This example is from Kevin Venzke, which he gave to show that Schulze (also) elects B and so fails this criterion. It doesn't bother me very much. MCA and Bucklin elect C. It is more Condorcetish and has a less severe later-harm problem than MCA, Bucklin, or Cardinal Ratings (aka Range, Average Rating, etc.) 40: AB 35: B 25: C Approval scores: A40, B75, C25 Approval Opp.: A35, B25, C75 Top-ratings scores: A40, B35, C25 They elect B, but SMD,FPP(w) elects the Condorcet winner A. It seems a bit less vulnerable to Burial strategy than Schulze. 46: AB 44: BC (sincere is BA) 05: CA 05: CB Approval scores: A51, B95, C54 Approval Opp.: A49, B05, C46 Top-ratings scores: A46, B44, C10. In this admittedly not very realistic scenario, no candidate is disqualified and so A wins. Schulze elects the buriers' favourite B. Chris Benham Send instant messages to your online friends http://au.messenger.yahoo.com Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Worst Voting Method
Very bad is the Supplementary Vote used to elect some mayors in the UK. It is like the Contingent Vote (one trip to the polls TTR) except voters are only allowed to rank 2 candidates. Kevin Venzke wrote: I don't see how this is very bad. I could see how you might think it is easily improved. But is this method better or worse than Approval? Is it better or worse than FPP? Kevin, The question of the precise ranking of the worst single-winner methods doesn't interest me very much. I just mentioned it as a method in use with absurd arbitrary features/restrictions that is dominated (in terms of useful criterion compliances) by IRV. To reluctantly answer your question I suppose it isn't worse than FPP and is probably worse than Approval. I'd be much more interested in your reaction to my recent Range-Approval hybrid suggested methods, which after all use the concept of Approval Opposition which you invented. Chris Benham Send instant messages to your online friends http://au.messenger.yahoo.com Election-Methods mailing list - see http://electorama.com/em for list info
