Re: [EM] Intermediate RV rating is never optimal
Abd ul-Rahman Lomax wrote: bits and pieces At 05:33 AM 7/21/2007, Michael Ossipoff wrote: That's incorrect. It's exactly the same in RV as in Approval. In your example, with B at your Approval cutoff, it doesn't matter how you rate B. In what I wrote, B was not at the voters approval cutoff. I didn't give an approval cutoff. Approval cutoff is an artificial insertion; it's a device for converting range ratings to approval votes. This is the situation described: The voter prefers ABC, with the preference strength between A and B being the same as the strength between B and C. There is nothing here about Approval cutoff, there is nothing that says that the voter does or does not approve of *any* candidate. I think we safely say that max-rating a candidate is equivalent to approving that candidate. Ossipoff confused the fact that the candidate was intermediate between A and C in sincere rating, i.e., being midrange, with being at your Approval cutoff. If the preference strength between A and B is weaker than that between B and C then with the winning probabilities being equal (or unknown) then the voter's best strategy is to max-rate A and B. If instead the preference strength between B and C is weaker, the voter does best to min-rate B and C (and of course max-rate A). Since the situation you describe is at the border of these two (max-rate B or min-rate B), we can say that B is at your approval cutoff. And, quite clearly, it *does* matter how you rate B in some scenarios; for example, if the real pairwise election is between A and B, then the optimum vote is to rate B at minimum. And if it is between B and C, then the optimum vote is to rate B at maximum. Of course it can matter after the fact, but with both possible real pairwise elections being equally likely at the time of voting, in Abd's scenario it probabilistically makes no difference what rating the voter gives B. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] RV comments
Abd ul-Rahman Lomax wrote: At 07:20 AM 7/20/2007, Michael Ossipoff wrote: Say, for the moment, we disregard the fact that the SU claims depend on sincere voting, and that sincere voting is nearly always suboptimal in RV. Ossipoff continually makes this claim. It's false. Suboptimal is the trick. It is suboptimal, true, from the point of view of the individual voter maximizing his or her own personal utility, *in some scenarios.* In others, it is clearly optimal to vote sincerely. Can we please have an example of one of these other scenarios that shows that Mike Ossipoff's claim is false? I think Warren Schudy put it well in a July 2007 draft paper: Range voting is a generalisation of approval voting where you can give each candidate any score between 0 and 1. Optimal strategies never vote anything other than 0 or 1, so range voting complicates ballots and confuses voters for little or no gain. If I prefer ABC, and those are the only options, it's clear that I optimize my expectation by voting A max, B min, but where do I rate B? ... Where do I rate B? Well, if the B utility is midway between A and C, we can define a sincere rating of B as 50%. If we have rated A max and C min. However, that max and min rating is itself a full disclosure of the utilities, the ratings have been normalized to the election candidate set, causing loss of absolute utilities. It never hurts the voter personally to normalize in that way. That is only true (probabilistically) if both the B utility is *exactly* midway between A and C and also (as far as the voter knows) both A and C are equally likely to win. It is obvious that in practice the voter in Abd's example could be hurt personally by not voting B max if that causes C to win instead of B, or by not voting B min if that causes B to win instead of A. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Conditional Approval (was Does this method have a name?)
Forest, I had a quick look at this. It seems that when there are just three candidates and they are in a cycle it elects the Approval winner. Is that right? In that situation I prefer ASM. I think my favourite method that uses the same type of ballots as your Conditional Approval would be a version of ASM Elimination that uses the voters' original approval cutoffs while they make some distinction among remaining candidates and thereafter interprets the voters' ballots as approving all but the lowest ranked of the remaining candidates. Chris Benham Forest W Simmons wrote: In probability theory when partial info about a random variable is given, the resulting updated expections and probabilities are called conditional expectations and probabilities. In that spirit, instead of calling the updated approvals based on partial info reactive, from now on I'm going to call them conditional. So the (i,j) element of the conditional approval matrix approximates the approval that candidate i would get, given only that candidate j is the poll front runner. Now for an update on how to use this conditional approval matrix to choose an election winner. Previously, I suggested circling the highest number in each column, removing each row not having a circled number as well as the corresponding column, repeating the process until every row has exactly one circled number (not worrying about ties for now), and finally electing the candidate with the largest row minimum in the remaining matrix. For this update I would like to change the final step. By the time each row has exactly one circled number the set of candidates is partitioned into cycles of one or more candidates each of the type x0, x1, x2, ... x0 where candidate i follows candidate j in the cycle if and only if element i of column j is circled. Let's use X~Y to denote that X and Y are members of the same cycle. In the revised final step, elect the candidate X with the largest minimum conditional approval given Y over all candidates Y such that Y~X. In other words X maximizes Min over Y~X of CA(X,Y) where CA(X,Y) is the (X,Y) entry of the remaining conditional approval matrix. Ideally, each of the remaining candidates (after iteratively crossing out the rows and columnns of the conditional approval losers) would be a conditional approval equilibrium candidate, which would make each cycle consist of exactly one candidate. In that ideal case, the equilibrium candidate with the greatest approval would be the winner. But since the ideal case is too much to expect, we think of equilibrium cycles instead of equilibrium candidates, and go with the winner of the cycle that maximizes the min conditional approval of its cycle winner. Forest From: Forest W Simmons [EMAIL PROTECTED] Subject: Re: [EM] Does this method have a name? The reactive approval of candidate X relative to Y as defined below is supposed to approximate the approval that X would get given only that Y was ahead of all the other candidates in the polls. In other words, if there were zero info up until someone reveals that Y is the front runner, would you approve X or not? Suppose that under zero info your approval cutoff was below Y. Given the information that Y is the frontrunner, wouldn't it make sense to move your cutoff up to just below Y? On the other hand, suppose that under zero info you disapprove Y. Given the info that Y is the frontrunner wouldn't it make sense to move your cutoff down to just above Y? The move would be in reaction to the given information, hence the term reactive. So we define the reactive approval of X relative to Y as the number of ballots on which X would be approved if the voted approval cutoff were moved adjacent to (but not past) Y on each and every ballot. Let RA be the matrix whose entry in row i and column j is the reactive approval of candidate i relative to candidate j. Let's call this matrix the reactive approval matrix. Below I suggested one way of using this matrix to determine a winner. Here's a more interesting one: 1. Circle the largest number in each column of the RA matrix. 2. Cross out each row that has no circled element. 3. Cross out the columns that correspond to the rows that were crossed out. [These rows and columns represent straw men or false alarms, so to speak, since any poll indicating that they were ahead would be misleading.] 4. Repeat steps 2 and 3 until each remaining row has exactly one remaining circled element. 5. The winner is the candidate who has the largest row minimum in the remaining matrix. What do you think? Forest Here's an example that might clear up some questions: Suppose that the original ballot is A=BC=DE=F|G=HI=JK=L where | is the voter's marked approval cutoff. Then in calculating reactive approvals relative to C we move the approval cutoff adjacent to but not past the position shared by C
Re: [EM] Does this method already have a name?
Forest W Simmons wrote: Ballots are ordinal with approval cutoffs. Forest, I gather from your description of the method that the voters don't/can't give explicit approval cutoffs that allow them to rank among unapproved candidates. I say this because in the algorithm these cuttoffs are moved about with their 'original position' having no effect. Is that right? If so, it seems to me that they way you define the ballots somewhat mixes up the concepts of input and algorithm and maybe even strategy. The candidate with Maximum Minimal Reactionary Approval wins. A candidate's reactionary approval relative to another candidate is the approval she would get if the approval cutoff were moved adjacent to (but not past) the other candidate's position in the ballot order on every ballot. Am I correct in taking it that (a) sometimes the approval cutoff is moved so that some ballots 'approve' none of the candidates, and (b) the cutoff is never moved to a position where it distinguishes between candidates given the same rank? Chris Benham Forest W Simmons wrote: Ballots are ordinal with approval cutoffs. The candidate with Maximum Minimal Reactionary Approval wins. A candidate's reactionary approval relative to another candidate is the approval she would get if the approval cutoff were moved adjacent to (but not past) the other candidate's position in the ballot order on every ballot. So each candidate's score is her minimum reactionary approval relative to the other candidates. The candidate with the highest score wins. It turns out that when rankings are complete this method is equivalent to the common versions of MinMax. It doesn't get tripped up on Kevin's standard example against pure MMPO: 49 A 1 A=B 1 B=C 49 C Does it satisfy the FBC? Forest election-methods mailing list - see http://electorama.com/em for list info election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Student government - what voting system to recommend?
Howard Swerdfeger wrote: Tim Hull wrote: Condorcet, on the other hand, does not suffer from the center squeeze. However, it suffers from the opposite problem - the so-called Pro Wrestler or Loony syndrome in an election with a couple polarized candidates and a weak centrist or joke candidate. In my student government elections, I picture this being a candidate walking around campus in a clown suit and winning based on becoming everybody's #2. Also, Condorcet's later-no-harm failure may mean people give a less sincere ranking than in IRV, though this failure is far less so than in range. This is a potential problem with all pure Condorcet methods. It might be able to be overcome with some restrictions Candidate must have 5% first preference votes or be one of the top 5 candidates in number of first preference votes. Or some other restriction might help. I can see why this is a marketing/propaganda problem, but not why it is a *real* problem. One reason why not is that Condorcet gives serious candidates incentive to contest the centre so if the election is serious then at least one serious centrist will run and one will win. If the election isn't serious then why is polarised candidate necessarily a better winner than a weak centrist or even a joke candidate? While I agree party lists are rotten. there are lots of other multi winner PR systems, that don't require a party list MMP where the top-up comes from the best of the losers. How exactly does this version of MMP work? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Student government - what voting system to recommend?
Tim Hull wrote: Regarding IRV, I do know it isn't ideal. In fact, if someone can show me it's necessarily worse than plurality, I'd just stick with plurality in single-winner and use STV in multi-winner. Plurality's only advantages over IRV are just a lot of monotonicty and mathematical elegance properties. IRV's advantages over Plurality: meets Majority for Solid Coalitions, Dominant Mutual Third, Condorcet Loser, Clone-Winner. The incentive for the voter to use the Compromise strategy is much much weaker than in Plurality. On this topic, does anyone know of a modified, kind-of-Condorcet-but-not-quite method which preserves later-no-harm? A method that would well handle all the 3-candidate examples you (Tim) and Juho have been trading is one where the voters can give an approval cutoff in their rankings. Rankings below the 'approval' cutoff cannot harm candidates ranked above it. 1. Voters rank candidates, truncation allowed but otherwise equal-preferences not, and voters give an 'approval' cutoff. Default placement is just above strict bottom or truncated candidates. 2. If one (remaining) candidate X is top-ranked (among remaining candidates) on more than half the (unexhausted) ballots, then elect X. 3. If not eliminate and drop from the ballots the least approved candidate. Then ignore ballots that make no preference distinction among remaining candidates (as 'exhausted') in resetting the majority threshold. Ballots that no longer make any explicit approval distinction among remaining candidates are now given the default placement as if though the eliminated candidate/s had never existed. 4. Repeat until there is winning X.. To answer your question more specifically, you might find CDTT methods interesting. http://nodesiege.tripod.com/elections/#methcdtt The CDTT is a set of candidates defined by Woodall to include every candidate A such that, for any other candidate B, if B has a majority-strength beatpath to A, then A also has a majority-strength beatpath back to B. (See Schulze #methsch for a definition of a beatpath.) Another definition (actually, the one Woodall chooses to use) of the CDTT is that it is the union of all minimal sets such that no candidate in each set has a majority-strength loss to any candidate outside this set. (Candidate A has a majority-strength loss to candidate B if v[b,a] is greater than 50% of the number of cast votes.) Markus Schulze proposed this set earlier, in 1997. His wording was to take the /Schwartz/ set resulting from replacing with pairwise ties, all pairwise wins with under a majority of the votes on the winning side. http://wiki.electorama.com/wiki/CDTT Limiting an election method's selection to the CDTT members can permit it to satisfy the Minimal Defense criterion /wiki/Minimal_Defense_criterion (and thus the Strong Defensive Strategy criterion /wiki/Strong_Defensive_Strategy_criterion) and the Majority criterion for solid coalitions /wiki/Mutual_majority_criterion, while coming close to satisfying the Later-no-harm criterion /wiki/Later-no-harm_criterion. Specifically, the CDTT completely satisfies Later-no-harm /wiki/Later-no-harm_criterion in the three-candidate case, and failures can only occur in the general case when there are majority-strength cycles. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] maybe a new variant of Condorcet
peter barath wrote (18/04/2007): I call a subset of candidates a quasi-clone set, if: 1. they don't make up the whole set of candidates 2. for every candidate out of the set they are in the same winning relation with (all beat / all tie / all lose) (You can ask why to make the subsets at all, but I think this Rubicon is already crossed with the Smith-set, which is a special kind of quasi-clone sets.) This is similar to Forest Simmons' beat clone sets he uses in his Dec. 2004 sprucing up process idea. http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-December/014325.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-December/014326.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-December/014328.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-December/014330.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-December/014331.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-December/014354.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-December/014337.html Chris Benham Markus Schulze wrote: Dear Peter Barath, your proposal is very similar to Mike Ossipoff's subcycle rule. Please read: http://lists.electorama.com/pipermail/election-methods-electorama.com/1996-June/000494.html http://lists.electorama.com/pipermail/election-methods-electorama.com/1996-June/000532.html http://lists.electorama.com/pipermail/election-methods-electorama.com/1996-July/000572.html http://lists.electorama.com/pipermail/election-methods-electorama.com/1997-September/001532.html http://lists.electorama.com/pipermail/election-methods-electorama.com/1998-June/001721.html http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-February/014707.html Markus Schulze election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Approval-Sorted Margins(Ranking) Elimination
Brian Olson wrote: I'm trying to understand the details of this procedure. On Apr 16, 2007, at 12:03 PM, Chris Benham wrote: My current favourite plain ranked-ballot method is Approval- Sorted Margins(Ranking) Elimination: 1. Voters rank candidates, truncation and equal-ranking allowed. 2. Interpreting ranking above bottom or equal-bottom as 'approval', initially order the candidates according to their approval scores from the most approved (highest ordered) to the least approved (lowest ordered). I'm a little fuzzy on this step, it sounds like that reverse-IRV method of disqualifying the most-last-placed choice. Does ABCD mean I approve of all but D? If there are no other candidates then for the initial ordering (or seeding as the electowiki ASM entry puts it) yes. And I'd think ABC=D would mean I approve of A and B,.. Same answer. If there are no other candidates then C and D are ranked equal-bottom. The above in step 2 applies to both bottom and equal-bottom. ...but this statement seems to imply approval for all of A-D, unless perhaps there's E and F left unranked then it would approve A-D and not E,F Brian, is this exactly what you meant to write? 3. If any candidate Y pairwise beats the candidate next highest in the order (X) , then modify the order by switching the order of the XY pair (to YX) that are closest in approval score. Repeat until all the candidates not ordered top are pairwise beaten by the next highest-ordered candidate. So, said another way, if the intermediate total order is ABCDEF as ordered by approval counts, but more ballots rank CB than BC, and more ballots rank ED than DE, then if the approval count [difference] of B-C is less than D-E, then flop B and C in the intermediate order. Repeat fixing up the intermediate order, always with the closest approval count difference, until no neighbors in the intermediate order violate pairwise ranking winner. (This seems to be very much like a condorcet process, actually, is it ever different unless there's a tie?) Yes, ASM is a Condorcet method. And so of course is ASM(R)E. As I put it in my Apr.16 post: At some point in the process all except the candidates in the top-cycle will be eliminated,.. The top-cycle is the Smith set. 4. Eliminate and drop from the ballots the (now) lowest ordered candidate. 5. Repeat steps 2-4 until one candidate (the winner) remains. Thanks for taking an interest, Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] Approval-Sorted Margins(Ranking) Elimination
Hello, My current favourite plain ranked-ballot method is Approval-Sorted Margins(Ranking) Elimination: 1. Voters rank candidates, truncation and equal-ranking allowed. 2. Interpreting ranking above bottom or equal-bottom as 'approval', initially order the candidates according to their approval scores from the most approved (highest ordered) to the least approved (lowest ordered). 3. If any candidate Y pairwise beats the candidate next highest in the order (X) , then modify the order by switching the order of the XY pair (to YX) that are closest in approval score. Repeat until all the candidates not ordered top are pairwise beaten by the next highest-ordered candidate. 4. Eliminate and drop from the ballots the (now) lowest ordered candidate. 5. Repeat steps 2-4 until one candidate (the winner) remains. Simply electing the highest ordered candidate after step3 is ASM(Ranking): http://wiki.electorama.com/wiki/Approval_Sorted_Margins First seed the list in approval order. Then while any alternative X pairwise defeats the alternative Y immediately above it in the list, find the X and Y of this type that have the least difference D in approval, and modify the list by swapping X and Y. It is equivalent to ASM(R) in the situation where there are three candidates in the top cycle with no voter ranking all three above bottom (and in any election with just three candidates). The advantage of this over ASM(R) is that there is less truncation incentive and voters who rank all the viable candidates plus one or more others will normally face little or no disadvantage compared to informed strategists. At some point in the process all except the candidates in the top-cycle will be eliminated, and assuming three remain then from that point it will proceed like an ASM(R) election as though the over-rankers 'approve' their two most preferred candidates (of the 3 in the top cycle). An advantage it has over Winning Votes (BP, RP,River) is that it doesn't have a 0-info. random-fill incentive. Also unlike both WV and Margins it meets the Possible Approval Winner (PAW) criterion. 35: A 10: A=B 30: BC 25: C CA 55-45, AB 35-30, BC 40-25. In this Kevin Venzke example, if we assume that voters rank all approved candidates strictly above all others then it isn't possible for B to be approved on more ballots than A. WV and Margins elect B. ASM(R)E, like ASM(R) and DMC(R), elects C. It seems obvious that ASM(R)E meets Minimal Defense. http://nodesiege.tripod.com/elections/#critmd // If more than half of the voters rank candidate A above candidate B, and don't rank candidate B above anyone, then candidate B must be elected with 0% probability.// Referring to this definition, while A and B remain uneliminated A will always be considered to be more 'approved' than B and of course A pairwise beats B, so B will always be ordered below A and so must at some point be eliminated. Chris Benham // election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] final support
Forest W Simmons wrote (31/03/2007): So far, the three most promising measures of defeat strength for Beatpath and the other immune methods are ... 1. Winning Votes: the number of ballots in favor of the pairwise win. 2. Total Approval: the number of ballots on which the pairwise winner is approved. The Beatpath, Ranked Pairs, and River formulations of DMC make use of this measure of defeat strength. 3. Approval Against: the number of ballots on which the pairwise winner is approved but the defeated alternative is not approved. I suggest that we combine these three measures, and call the resulting measure Final Support, because it is an indication of the ratification support that the victor of a pairwise contest would receive, given that the defeated alternative is out of the picture. 4. Final Support: the number of ballots on which the victor of a pairwise contest is either approved or ranked above the defeated alternative (or both). I suggest that River(fs) would be worth looking into, starting with all of the troublesome three candidate scenarios. Forest, Why isn't Approval Margins: the number of ballots on which the pairwise winner is approved minus the number of ballots on which the pairwise defeated alternative is approved on your list of most promising measures of defeat strength..? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] One example of a wording problem
Michael Ossipoff wrote: Chris wrote: If the balloting rules don't allow the voters to fully express their intended ranking, then we assume that the voters vote to express as much of it as the balloting rules allow, giving priority to expressing as many of their intended strict pairwise preferences as possible I reply: If we take that literally, then, if the actual method is Approval, then the actual ballot has to approve half of the candidates in the intended ranking, because that's the way to expressing as many of that ranking's pairwise preferences as possible. But that isn't what you intend. Mike, Yes you are right, thanks. If there are 4 candidates A,B,C,D, I want both A and ABC to be both allowable interpretations on an Approval ballot of the 'intended ranking' ABC. But A only expresses 3 pairwise preferences (AB, AC, AD) whereas AB expresses 4 (AC,AD, BC, BD). Also ABC only expresses 3 (AD, BD,CD). In a way what I said maybe wasn't ridiculous, but it wasn't and isn't what I intend/ed. I'll re-think it. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] Venzke system for applying criteria, FARCS
This current discussion was sparked by my remark (March 17, 2007): I share the Venke (similar to Woodall's) approach that the criteria should assume that the voters intend to submit a ranked ballot (maybe truncated, maybe with some equal-ranking) and that voters fill out their actual (maybe restricted) ballots in a way that is consistent with their intended ballots, and when ballot restrictions prevent voters from fully voting their intended ranked ballots the criteria are based on the intended ballots. Mike Ossipoff responded (March 20, 2007): What an elaborate counterfactual story. It’s amazing what lengths to which some people will go, to make Plurality fail Condorcet’s Criterion without mentioning preference. I've already answered about that. It's based on a privileged balloting system. My criteria make no mention of any balloting system. Though you go to great lengths to avoid mentioning preferences, you don't mind saying that the voter intends to vote a ranking, when s/he votes in Plurality. I've talked to voters, and many of them are adamantly opposed to any voting system other than Plurality. They don't intend to vote a ranking when they vote Plurality. And that's only part of the counterfactual nature of your fictitious-rankings system of criteria. Mike, notice that I specified that the voters' intended ranking is maybe truncated. It doesn't matter if the voters subjectively don't have rank in their vocabulary: those that plan to cast a valid Plurality vote intend to rank a single candidate above all others. Whatever balloting system is used all votes (that make any distinction among the candidates) contain some (logically implicit) ranking data and there is no other type of data that they all contain, so I can't see that your reference to a privileged balloting system is a meaningful criticism. Mike apparently didn't think that I or Kevin had properly defined Kevin's way of applying criteria, so he came up with a definition of what he called Fictitiously Assumed Rankings Criteria System (FARCS). Here is my attempt at a definition of the Venzke approach to applying criteria with Mike-satisfying precision: Venzke rules for demonstrating a voting method's failure of criterion X: Criteria are written in the form of if A, then B where A refers to some stipulation about the votes and B refers to something about the election result that must happen. It is assumed that the voters have an 'intended ranking' of the candidates that may be truncated and/or include some above-bottom equal ranking. By definition, if the balloting rules allow the voters to fully express this ranking then that is what the voters will do. The A part of a criterion refers to this intended ranking. If the balloting rules don't allow the voters to fully express their intended ranking, then we assume that the voters vote to express as much of it as the balloting rules allow, giving priority to expressing as many of their intended strict pairwise preferences as possible followed by expressing as many of their intended pairwise equal-preferenes (indifferences) as possible. If the voters can only express some or all of their intended ranking by giving preference data that isn't on their intended ranking, then we assume that they do so in a way that contradicts their intended ranking as little as possible. If in testing for a method's compliance with criterion X, we can follow the above rules/assumptions and show an example of A and not B, then we have proved that the method fails criterion X. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] A definition for your criteria system
Michael Ossipoff wrote: FARCS stands for Fictitiously Assumed Rankings Criteria System. Because no FARCS advocate on EM has defined FARCS, I’m going to define it in this posting. Definition of FARCS, consisting of instructions for writing a criterion failure example in the FARCS system: 1. Specify a set of voter rankings that complies with the criterion’s premise’s stipulations about rankings. 2. Specify each voter’s actual vote (using the actual balloting system of the method being tested) in such a way that s/he doesn’t vote X over Y when your ranking for that voter ranks Y over X. 3. If you can thereby specify actual votes that give a result that doesn’t comply with the criterion’s requirement, then you have written a successful failure example. [end of FARCS definition] Regarding (1), I'm not sure exactly what the criterion’s premise’s stipulations about rankings means. Your point (2) is inadequate, because it could be that the voter intends to strictly rank some candidates while the actual used method allows but not compels the voter to equal-rank them. By this definition it could be possible to create a criterion failure example by having actual votes with equal-ranking where the voter intended strict ranking, even though the the used method would have allowed the intended strict ranking. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] More FARCS problems
Michael Ossipoff wrote: Chris said that people arrive at the polls intending to vote a certain way in a rank method, and then find out that it's (say) Plurality or Approval. Say it's Plurality. Their ranking that they arrive with would reasonably have their favorite in 1st place (Yes, I know it's a no-no to speak of preference). Now, upon finding out that it's Plurality, they have strategic reason to give their one vote to a lower choice compromise. But FARCS has them voting consistent with their rankings, so that their 1st ranked candidate must be the one they vote for in Plurality. Yes. All the strategising (if any) is supposed to only happen between their sincere preferences and their 'intended ranking'. Or, if it's known to be a Plurality election, do they come to the polls intending to vote a ranking that has their Plurality compromise at the top of the ranking? Yes. What about FBC? One must not get a better result by burying one's favorite. But FARCS and votes-only doesn't allow speaking of favorites. So, what is it then, does top-ranked replace favorite? But then, if the actual ballot has to be consistent with the ranking, the top ranked candidate can't be buried. So how could there be an FBC test? Kevin's Sincere Favourite criterion seems fine to me. If the voter's intended ranking is A=BC and this results in neither of A or B winning, but some other intended ranking with one or both of A and B not given top preference results in one of them winning, then SF is failed. *Sincere Favorite*. /Suppose a subset of the ballots, all identical, rank every candidate in S (where S contains at least two candidates) equal to each other, and above every other candidate. Then, arbitrarily lowering some candidate X from S on these ballots must not increase the probability that the winner comes from S./ A simpler way to word this would be: /You should never be able to help your favorites by lowering one of them./ http://nodesiege.tripod.com/elections/ Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] RE : Chris: Approval
Kevin Venzke wrote: Aside from that, why is it ok to speak of intent, but not preference? Intent is post-strategy. Here's an example of the process: 1. Say my sincere preferences are ABCDE. 2. Then I apply whatever reasoning and decide that I will be voting DAB and truncate the rest. Then that DAB is my intended vote. 3. At this point I the voter do not make any more decisions. Suppose the ballot format is such that I can only vote for two candidates equally and nobody else. Then my cast ballot is either D=A or D=B, according to arbitrary resolution. Kevin, Is this exactly what you meant to write? The way it is written, I don't see how D=B is a possible choice of cast ballot for the voter whose intended ranking is DAB. If D=B is possible, why not A=B? I would rather say (in your point 3) that if the method is approval the voter with an intended ranking of DAB (in this field of more than 3 candidates) makes an arbitrary choice between D or DA or DAB for his 'cast ballot'. Chris Benham Mike, --- Michael Ossipoff [EMAIL PROTECTED] a écrit : I share the Venke (similar to Woodall's) approach that the criteria should assume that the voters intend to submit a ranked ballot (maybe truncated, maybe with some equal-ranking) and that voters fill out their actual (maybe restricted) ballots in a way that is consistent with their intended ballots, and when ballot restrictions prevent voters from fully voting their intended ranked ballots the criteria are based on the intended ballots. I've already answered about that. It's based on a privileged balloting system. My criteria make no mention of any balloting system. But you also can't demonstrate that they are unambiguous for any possible election method. Though you go to great lengths to avoid mentioning preferences, you don't mind saying that the voter intends to vote a ranking, when s/he votes in Plurality. I've talked to voters, and many of them are adamantly opposed to any voting system other than Plurality. They don't intend to vote a ranking when they vote Plurality. Doesn't matter. That's not the point of speaking of intent. Could you demonstrate why Approval and 0-10 CR fail Condorcet's Criterion, in your system? Personally I don't have anything to add on these topics. I gave an example of dealing with CR, and acknowledged that Approval is a weak point. Aside from that, why is it ok to speak of intent, but not preference? Intent is post-strategy. Here's an example of the process: 1. Say my sincere preferences are ABCDE. 2. Then I apply whatever reasoning and decide that I will be voting DAB and truncate the rest. Then that DAB is my intended vote. 3. At this point I the voter do not make any more decisions. Suppose the ballot format is such that I can only vote for two candidates equally and nobody else. Then my cast ballot is either D=A or D=B, according to arbitrary resolution. So an advantage of using intent over preference is that the voter only has input at one stage. That's exactly as if you were only considering cast ballots, except that you don't have to worry that perhaps the voter was not allowed by the ballot to cast his preferred vote. Preference and intent really take the same approach to not having to worry about ballot restrictions, in that they both try to regard voter input before it hits the paper. Kevin Venzke election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Chris: Approval
Michael Ossipoff wrote: Your definition of your criteria system sounds conversational and inexact. Could you demonstrate why Approval and 0-10 CR fail Condorcet's Criterion, in your system? Aside from that, why is it ok to speak of intent, but not preference? Speaking of preference is an ok alternative, but we don't necessarily want to worry about what might be 'sincere preferences' that are voluntarily not voted. Chris continues: [after naming a long list of criteria met by Approval] But it fails Majority Favourite and Majority Loser Do you mean those criteria with your fictitious rankings? Yes. I've never denied that rank methods can add advantages not available in Approval. I've even said that I myself would prefer a good rank method for our public elections, though I myself, as a voter, would be content with Approval. It would be a nice luxury to rank the best candidates, but I don't really care which one of the best candidates wins. That is your individual inclination, one which is very convenient for an Approval advocate. I'd said: Obviously majority rule is violated by an outcome that is contrary to what a majority have voted that they want. For instance, if a majority vote B over A, then we can assume that, if A or B wins, they vote that it be B. Chris says: That is reasonable, and granted for the sake of argument. That implies that you agree with Kevin Venzke that Minimal Defense(MD) must be met It does?? I don't agree with Keviln Venzke that Minimal Defense (MD) must be met. From Levin's page: *Minimal Defense*. /(Due to Steve Eppley.)/ /If more than half of the voters rank candidate A above candidate B, and don't rank candidate B above anyone, then candidate B must be elected with 0% probability./ Steve Eppley has defined and discussed Minimal Defense here http://alumnus.caltech.edu/%7Eseppley/ and here http://alumnus.caltech.edu/%7Eseppley/Strategic%20Indifference.htm. Satisfaction of this criterion implies compliance with Mike Ossipoff's /strong defensive strategy criterion/, although the reverse is not necessarily true. That criterion can be found here http://www.barnsdle.demon.co.uk/vote/stfree.html. http://nodesiege.tripod.com/elections/ It does?? I don't agree with Keviln Venzke that Minimal Defense (MD) must be met. I'd be interested in seeing an example of MD failure that you agree (or are content) with. Chris continues: [Approval] is very vulnerable to disinformation campaigns That's a vague statement that could be said of many methods, including some that Chris likes. My statement lacked details, but that doesn't make it vague. I've elaborated this criticism of Approval a few times before. Say in the lead-up to the election two candidates have announced that they will run, and accurate polling of voters' voting intentions shows A52%, B48%. Say the media hate A, so others that hate A nominate a third candidate C who is anathema to A's supporters (or at least some of them). Then those that hate A set about giving C a high profile and publishing some fake polls that suggest that C has some chance to win. This frightens some of the A supporters into approving B, causing A to win. 47: A 05: AB (disinformed timid AB preferrers) 46: B 02: CB Approval: B53, A52, C2. What methods that I like do you have in mind as being comparably vulnerable to disinformation campaigns? Sincere preferences: 40: A 29: BC 31: CB The C voters vote C B. The B voters vote only B. B wins by defection. Chris, can you find a majority who is being robbed of victory here? No, but if 21 or more of the C voters also defect the sincere BC majority solid coalition is robbed of victory and the sincere majority loser wins. I've repeatedly asked you to show that Approval and CR pass or fail Condorcet's Critrerion, by your fictitious-ranking approach. You never did. I asked Chris. He couldn't either. In your example say the 'intended rankings' are 40: A 29: BC 31: CB On these intended rankings, C is the CW. On arriving at the polling place we pretend that those who were intending to rank BC or CB are surprised to find that they have to use 2-slot ballots, so they each make an arbitrary choice whether to approve (consistent with their intended rankings) one candidate or two. This could result in these actual cast approval ballots: 40: A 29: B 10: CB 21: C Approvals: A40, B39, C31. A wins, failing Condorcet. (This is the same set of cast ballots as in the defection backfires because of too many defectors example). Chris Benham I election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] MAMPO is probably better than MDDA
Kevin Venzke wrote (Feb 22,2007): Hi. This is the definition of MAMPO: 1. A candidate's opposition score is equal to the greatest number of votes against him in any pairwise contest. 2. The voter ranks; those ranked are also approved. 3. If more than one candidate is approved by a majority, elect the one of these with the lowest opposition score. 4. Otherwise elect the most approved candidate. MAMPO satisfies FBC, SDSC, and SFC like MDDA does. But MAMPO also satisfies Woodall's Plurality criterion. Kevin, I'm interested in your opinion of my stab at something similar that meets Irrelevant Ballots: 1 and 2 as for MAMPO. 3. Give each candidate a score that is equal to its approval score minus its opposition score. 4. Elect the candidate with the highest score. With sensible approval strategy, this seems to 'perform well' (in terms of strategic criteria) with 3 or 4 candidates. The approval component seems to easily rescue MMPO from its greatest embarrassments. One hope is that the truncation incentive of Approval and the random-fill incentive of MMPO will mostly cancel each other out. There may be some smarter way to combine approval and pairwise opposition scores, perhaps weighting them unequally. And if anyone likes it I'm open to a suggestion for a name. Chris Benham Hi. This is the definition of MAMPO: 1. A candidate's opposition score is equal to the greatest number of votes against him in any pairwise contest. 2. The voter ranks; those ranked are also approved. 3. If more than one candidate is approved by a majority, elect the one of these with the lowest opposition score. 4. Otherwise elect the most approved candidate. MAMPO satisfies FBC, SDSC, and SFC like MDDA does. But MAMPO also satisfies Woodall's Plurality criterion. Woodall's scenario showing that MDDA fails the latter: 20 ab 5 ba 24 bc 24 ca 9 dab 9 dbc 9 dca a,b,c are preferred to d by 49,49,48 voters respectively, which are not majorities, but ab by 62, bc by 67 and ca by 66, so that a, b and c are all disqualified. Thus MDDA elects d. But d has 27 votes in total, and so is debarred by b who has 29 first-preference votes. MAMPO manages to elect B since D lacks majority approval, and 62 is the lowest maximum such score. For what it's worth. I think MAMPO does a fairly reasonable thing in only deviating from approval when multiple candidates have a majority, and then only in favor of one of the candidates that has a majority! Kevin Venzke ___ election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Chris reply
more than what the Approval method guarantees--as much as I like Approval. For me, as a voter, Approval would be fine. It’s the other progressives who need a good rank method, because they tend to have poor judgment about approving some sleazy crook known as a Democrat lesser-evil. My concern is that they might keep doing the same thing if we had the Approval method. Approval is still definitely worth a try, because they might stop voting for the Democrat when they notice that (say) Nader is outpolling the Republican. But a good rank method homes in on the voter median immediately, instead of after a few elections. And it isn’t proved that the LO2E progressives will have the courage to ever stop voting for the Democrat. Those are the reasons why I’d like a good rank method, as my first choice for our public political elections. Without informed strategy Approval guarantees not much. Hopefully a set of democratic reforms that include a good rank method will attract a lot of new voters with more courage and sense than your LO2E progressives. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Trees and single-winner methods
Juho wrote: Here's one more election method for you to consider Let's start from a Condorcet method (it doesn't matter much which one). Then we allow the candidates to form groups. Each group will be handled as if it was a single candidate. I reject this on the same grounds that I reject the candidate withdrawal option (in say IRV) and Asset Voting: I am only interested in single-winner methods where the result is purely determined (as far as possible) by voters voting, and not by the machinations of candidates/parties. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Possible Approval Winner set/criterion (was Juho--Margins fails Plurality. WV passes.)
Juho wrote: The Possible Approval Winner criterion looks actually quite natural in the sense that it compares the results to what Approval voting could have achieved. I'm glad you think so. The definition of the criterion contains a function that can be used to evaluate the candidates (also for other uses) - the possibility and strength of an approval win. This function can be modified to support also cardinal ratings. In the first example there is only one entry (11: AB) that can vary when checking the Approval levels. B can be either approved or not. In the case of cardinal ratings values could be 1.0 for A, 0.0 for C and anything between 0.0001 and 0. for B. Or without normalization the values could be any values between 0.0. and 1.0 as long as value(A) value(B) value (C). With the cardinal ratings version it is possible to check what the original utility values leading to this group of voters voting AB could have been (and if the outcome is achievable in some cardinal ratings based method, e.g. max average rating). This concept looks vulnerable to some weak irrelevant candidate being added to the top of some ballots, displacing a candidate down to second preference and maybe thereby causing it to fall out of the set of possible winners. It probably has other problems regarding Independence properties, and I can't see any use for it. Chris Benham The Possible Approval Winner criterion looks actually quite natural in the sense that it compares the results to what Approval voting could have achieved. The definition of the criterion contains a function that can be used to evaluate the candidates (also for other uses) - the possibility and strength of an approval win. This function can be modified to support also cardinal ratings. In the first example there is only one entry (11: AB) that can vary when checking the Approval levels. B can be either approved or not. In the case of cardinal ratings values could be 1.0 for A, 0.0 for C and anything between 0.0001 and 0. for B. Or without normalization the values could be any values between 0.0. and 1.0 as long as value(A) value(B) value (C). With the cardinal ratings version it is possible to check what the original utility values leading to this group of voters voting AB could have been (and if the outcome is achievable in some cardinal ratings based method, e.g. max average rating). The max average rating test is actually almost as easy to make as the PAW test. Note that my description of the cardinal ratings for candidate B had a slightly different philosophy. It maintained the ranking order of the candidates, which makes direct mapping from the cardinal values to ordinal values possible. The results are very similar to those of the approval variant but the cardinal utility values help making a more direct comparison with the original utilities of the voters. Now, what is the value of these comparisons when evaluating the different Condorcet methods. These measures could be used quite straight forward in evaluating the performance of the Condorcet methods if one thinks that the target of the voting method is to maximise the approval of the winner or to seek the best average utility. This need not be the case in all Condorcet elections (but is one option). There are several utility functions that the Condorcet completion methods could approximate. The Condorcet criterion itself is majority oriented. Minmax method minimises the strength of interest to change the selected winner to one of the other candidates. Approval and cardinal ratings have somewhat different targets than the majority oriented Condorcet criterion and some of the common completion methods, but why not if those targets are what is needed (or if they bring other needed benefits like strategy resistance). I find it often useful to link different methods and criteria to something more tangible like concrete real life compatible examples or to some target utility functions (as in the discussion above). One key reason for this is that human intuition easily fails when dealing with the cyclic structures (that are very typical cases when studying the Condorcet methods). In this case it seems that PAW and corresponding cardinal utility criterion lead to different targets/utility than e.g. the minmax(margins) required additional votes to become the Condorcet winner philosophy. Maybe the philosophy of PAW is to respect clear majority decisions (Condorcet criterion) but go closer to the Approval/cardinal ratings style evaluation when the majority opinion is not clear. You may have different targets in your mind but for me this was the easiest interpretation. Juho P.S. One example. 1: AB 1: C Here B could be an Approval winner (tie) but not a max average rating winner in the ranking maintaining style that was discussed above (since the rating of B must be marginally smaller than the rating
Re: [EM] Chris reply
Michael Ossipoff wrote: Chris-- You wrote: Mike, Does this compromising one C voter have to unapprove C? I reply: No. Referring to this example, 52: AC (offensive order-reversal) 100: BA 50: C/B You continued: ACBA. Approvals: A152, C102, B100. AC 152-50, CB 102-100, BA 150-52 DMC and ASM elect A. I reply: You continued: Here if one C|B changes to B|C I reply: It doesn’t matter if it’s B/C or BC, because, as I said, the approval votes don’t come into play, because there’s already an unbeaten candidate, B, who therefore wins. You continued: then DMC just becomes indecisive with B and C on the same approval score and pairwise tied. I reply: Pairwise tied, yes. Indecisive, no. B wins because B is the only unbeaten candidate. According to DMC’s rules, B wins. If the C voters vote BC, approving both, then, as you said, they make a pair-wise tie between B and C. B beats A and pair-ties C. B wins as the only unbeaten candidate. The Approval scores don’t come into play, because there already is an unbeaten candidate. At least that’s how I understood the rules of DMC: If no one is unbeaten, repeatedly eliminate the least-approved candidate till someone is unbeaten. Yes, that is doubtless the best way: elect the Schwartz winner. If I’ve misunderstood DMC’s rules, tell me the correct DMC rules. No, looks like my mistake. I'll give some reply to the rest later. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Possible Approval Winner set/criterion (was Juho--Margins fails Plurality. WV passes.)
Juho wrote: I don't see any strong need to use the PAW criterion (or corresponding ratings variant) for strategy resistance or for election target reasons but they seem possible. They add complexity, but if justified for some reason, then why not. I'll try to think more and come back if needed. I'm not suggesting that PAW be explicitly made part of the rules of any method, and the PAW criterion is met by most methods including the simplest. So I don't see how it adds complexity. The Plurality criterion is about avoiding common-sense, maybe simple-minded but nonetheless very strong and (IMO)sound complaints from a significant subset of voters: the supporters of a candidate that pairwise beats the winner: X ranked alone in top place on more ballots than Y was ranked above bottom clearly equals 'X has more support than Y', so how can you justify X losing to Y?!. PAW tries to be a generalisation of Plurality, and less arbitrary because it doesn't talk about top preferences. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] All uncovered options may be definitely defeated
Jobst Heitzig wrote: Unfortunately, there is no method that elects an option which is both uncovered and has not definite majority against it, simply because such options might not exist: Example: Pairwise defeats ABCDA, DB, CA, hence covering relation DA Approval scores ABCD, hence definite defeats ABCD. It seems we have to decide whether we consider definite defeats or covering defeats more important... Jobst Since these Condorcet methods that meet Definite Majority (ASM, DMC, Smith//Approval) all meet Smith, then your concern about covering defeats can only be about situations with more than three candidates in the Smith/Schwartz set. For public political elections that for me is not a practical worry, whereas Definite Majority applies in many relatively common-place 3-candidate scenarios. Chris Benham Dear Chris, you wrote: TACC having that curious property and so electing B here shows that it spectacularly fails the Definite Majority criterion. Maybe that is forgivable for a FBC method like MAMPO, but not for a Condorcet method that bases its result on nothing but pairwise and approval information. You're perfectly right here. It was before we studied definite majorities and found DMC that I proposed TACC. Unfortunately, there is no method that elects an option which is both uncovered and has not definite majority against it, simply because such options might not exist: Example: Pairwise defeats ABCDA, DB, CA, hence covering relation DA Approval scores ABCD, hence definite defeats ABCD. It seems we have to decide whether we consider definite defeats or covering defeats more important... Jobst election-methods mailing list - see http://electorama.com/em for list info election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] DAMC
Jobst Heitzig wrote: Def. DAMC (Definite Absolute Majority Choice): -- Make a list of absolute majority size pairwise defeats. Process this list in order of descending approval score of the defeating option. Keep the defeat at hand iff (i) the defeated option is not already defeated by the kept defeats and (ii) the new defeat does not build a cycle with those defeats already kept. From those options not defeated in the end, elect the most approved one. In other words: We use River with defeat := absolute majority size defeat and defeat strength := approval score of defeating option and resolve the remaining ambiguity by Approval. I'm pretty sure that this method has the following properties: - monotonicity - clone-proofness - IPDA and ISDA - immunity from absulute majority complaints (in the above sense) - immunity from 2nd place complaints - the winner is never defeated with absolute majority by a more approved option or by the most approved contender. What I'm not sure about so far is whether using Beatpath or Ranked Pairs instead of River gives the same winner, and what would happen when we used the resorting or the definitively defeated version of DMC with absolute majority size defeats only. Jobst, Does this meet FBC/SF? Because I think something that fails Condorcet and Irrelevant Ballots and presumably Definite Majority would want to. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Possible Approval Winner set/criterion (was Juho--Margins fails Plurality. WV passes.)
Juho wrote (March7, 2007):
The definition of plurality criterion is a bit confusing. (I don't
claim that the name and content and intention are very natural
either :-).)
- http://wiki.electorama.com/wiki/Plurality_criterion talks about
candidates given any preference
- Chris refers to above-bottom preference votes below
/If the number of ballots ranking /A/ as the first preference is
greater than the number
of ballots on which another candidate /B/ is given any preference,
then /B/ must not be elected./
Electowiki definition could read: If the number of voters ranking A
as the first preference is greater than the number of voters ranking
another candidate B higher than last preference, then B must not be
elected.
Yes it could and to me it in effect does (provided last means last or
equal-last) The criterion come
from Douglas Woodall who economises on axioms so doesn't use one that
says that with three candidates
A,B,C a ballot marked ABC must always be regarded as exactly the same
thing as AB truncates. He
assumes that truncation is allowed but above bottom equal-ranking isn't.
A similar criterion of mine is the Possible Approval Winner criterion:
Assuming that voters make some approval distinction among the
candidates but none among those
they equal-rank (and that approval is consistent with ranking) the
winner must come from the set of
possible approval winners.
This assumes that a voter makes some preference distinction among the
candidates, and that truncated
candidates are equal-ranked bottom and so never approved.
Looking at a profile it is very easy to test for: considering each
candidate X in turn, pretend that the
voters have (subject to how the criterion specifies) placed their
approval cutoffs/thresholds in the way
most favourable for X, i.e. just below X on ballots that rank X above
bottom and on the other ballots
just below the top ranked candidate/s, and if that makes X the (pretend)
approval winner then X is
in the PAW set and so permitted to win by the PAW criterion.
11: AB
07: B
12: C
So in this example A is out of the PAW set because in applying the test
A cannot be more approved
than C.
IMO, methods that use ranked ballots with no option to specify an
approval cutoff and rank among
unapproved candidates should elect from the intersection of the PAW set
and the Uncovered set
One of Woodall's impossibility theorems states that is impossible to
have all three of Condorcet,
Plurality and Mono-add-Top. MinMax(Margins) meets Condorcet and
Mono-add-Top.
Winning Votes also fails the Possible Approval Winner (PAW) criterion,
as shown by this interesting
example from Kevin Venzke:
35 A
10 A=B
30 BC
25 C
AB 35-30, BC 40-25, CA 55-45
Both Winning Votes and Margins elect B, but B is outside the PAW set{A,C}.
Applying the test to B, we get possible approval scores of A45, B40, C25.
ASM(Ranking) and DMC(Ranking) and Smith//Approval(Ranking) all meet the Definite
Majority(Ranking) criterion which implies compliance with PAW. The DM(R) set is
{C}, because interpreting ranking (above bottom or equal-bottom) as approval,
both
A and B are pairwise beaten by more approved candidates.
Chris Benham
election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Juho--Margins fails Plurality. WV passes.
Michael Ossipoff wrote: In a posting to a different mailing list, Markus pointed out that margins fails the Plurality Criterion, and that wv Condorcet passes the Plurality Criterion. Yes. 11: AB 07: B 12: C A Woodall example that applies. Margins elects A, yet C has more top preference votes than A has above-bottom preference votes. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] UncAAO
with a Nash equilibrium, no matter where the B faction puts its approval cutoff. 49 C 24 BA 27 AB As in wv, no defensive strategy is needed under zero info conditions. But if you suspect that X is the CW, and you could live with X, then a prudent move would be to approve X and above. For what it's worth, this all applies at least as well to ASM and DMC. Of course some of the sincere BA preferrers have to at least truncate for A not to be alone in the Smith set. When the ballot-style allows voters to rank among unapproved candidates ASM and DMC are my co-equal favourites, and when it doesn't I prefer ASM. http://wiki.electorama.com/wiki/Approval_Sorted_Margins Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] UncAAO
Forest W Simmons wrote: UncAAO stands for Uncovered, Approval, Approval Opposition. Here's how it works: For each candidate X, if X is uncovered, then let f(X)=X, else let f(X) be the candidate against which X has the least approval opposition, among those candidates that cover X. Start with the approval winner A and apply the function f repeatedly until the output equals the input. This fixed point of f is the method winner. Is there any chance that someone who understands this will translate it into plain English? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] UncAAO
Forest W Simmons wrote: Here are the main advantages of UncAAO over other Condorcet methods: 1. It is resistant to manipulation ... more so than Beatpath or Ranked Pairs, if I am not mistaken. 2. It always chooses from the uncovered set. 3. It is at least as easy as Ranked Pairs to describe. No mention of the possibility of cycles is needed, since the covering relation is transitive. 4. It is easier than Ranked Pairs or Beatpath to compute. One never has to check for cycles, since the covering relation is transitive. 5. It takes into account strength of preference through appropriate use of Approval information. With regards to point 1, consider the following example (sincere votes): 45 ACB 35 BCA 20 CAB Here C is the CW. Is this example right? This is not a Nash Equilibrium for Margins, Ranked Pairs, PC, etc. because the A faction can improve its lot unilaterally by reversing CB to BC. Under winning votes the C faction can take defensive action and truncate to 20 C. The resulting position is a Nash Equilibrium. Taking such defensive action causes B to win, so why would they want to do that when they prefer A to B? And I don't see why the resulting position is a Nash Equilibrium (according to the definition I googled up), because the sincere CA faction can change the winner from B to A by changing their votes from C to CA. * *DEFINITION: Nash Equilibrium* If there is a set of strategies with the property that no player can benefit by changing her strategy while the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute the Nash Equilibrium. *http://william-king.www.drexel.edu/top/eco/game/nash.html Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] A few concluding points about SFC, CC, method choice, etc.
Pasting from Mike's page: /Some definitions useful in subsequent criteria definitions:/ A voter votes X over Y if he votes in a way such that if we count only his ballot, with all the candidates but X Y deleted from it, X wins. [end of definition] Voting a preference for X over Y means voting X over Y. If a voter prefers X to Y, and votes X over Y, then he's voting a sincere preference. If he prefers X to Y and votes Y over X, he's falsifying a preference. A voter votes sincerely if he doesn't falsify a preference, and doesn't fail to vote a sincere preference that the balloting rules in use would have allowed him to vote in addition to the preferences that he actually did vote. [end of definition] Strategy-Free Criterion (SFC): /Preliminary definition: /A Condorcet winner (CW) is a candidate who, when compared separately to each one of the other candidates, is preferred to that other candidate by more voters than vice-versa. Note that this is about sincere preference, which may sometimes be different than actual voting. SFC: If no one falsifies a preference, and there's a CW, and a majority of all the voters prefer the CW to candidate Y, and vote sincerely, then Y shouldn't win. [end of definition] Michael Ossipoff wrote: Kevin and Chris posted their criteria that they incorrectly claimed equivalent to SFC. These same alternative SFCs have been posted to EM before and thoroughly discussed before. In fact, we've been all over this subject before. So why don't you point us to where in the EM archive we can find this earlier discussion? Are they in your opinion equivalent for ranked-ballot methods? Though Chris's and Kevin's criteria clearly are not equivalent to SFC, maybe someone could write a votes-only cirterion that is. First of all, what's this obsession about votes-only? Some people worry that criteria that give the appearance that we have to read voters' minds to see if they are met are not the easiest to check for. Now, quite aside from that, the efforts to write a votes-only equivalent criterion seem motivated by a desire to not say things that happen to be what I want to say. I want SFC to be about the fact that that majority, because they all prefer the CW to Y, and because there's no falsification (on a scale sufficient to change the outcome), can defeat Y by doing nothing other than voting sincerely. To say it in a way that doesn't say that wouldn't be SFC. If someone wrote such a criterion, then I'd recognize it as a _test_ for SFC compliance, but not as SFC. When I say that a method passes or fails SFC, and someone says What's that?, then I want to tell them the SFC described in the paragraph before this one, the one that relates to the CW, no need for other than sincere voting by the majority and non-falsified voting by everyone else. If I worded it like Kevin or Chris, it wouldn't be self-evident why it's desirable to meet that criterion. Someone could suggest that I use an alternative as the criterion, and save my SFC as a justification. No, I want the criterion's value to be self-evident. Well its value as something distinct from the Condorcet criterion isn't self-evident to me. If this CWY majority can't elect the CW, why do they necessarily care if Y is elected or not? And the way you've dressed this up, I can't see how it really qualifies as a strategy criterion. How are the members of this CWY majority supposed to know whether or not anyone falsifies a preference? And if they do know what are they supposed to do about it? From Steve Eppley's MAM page: /truncation resistance/ Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm: Define the sincere top set as the smallest subset of alternatives such that, for each alternative in the subset, say x, and each alternative outside the subset, say y, the number of voters who sincerely prefer x over y exceeds the number who sincerely prefer y over x. If no voter votes the reverse of any sincere preference regarding any pair of alternatives, and more than half of the voters rank some x in the sincere top set over some y outside the sincere top set, then y must not be elected. (This is a strengthening of a criterion having the same name promoted by Mike Ossipoff, whose weaker version applies only when the sincere top set contains only one alternative, a Condorcet winner.) This makes some sense as a strategy criterion, being about deterring a faction from truncating against the members of the sincere Smith set. The weaker version ascribed to you seems easier to test for. How does that version differ from your present SFC? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Randomized MCA, new weird voting method idea
Warren Smith wrote:
I'll describe a new voting method. I'm not sure if it is brilliant
or crazy. I'm also unsure how to analyse it.
1. Forest Simmons has often advanced the idea of using randomness in voting
methods inspire more voter honesty. (Lottery methods.)
2. IEVS (my simulator - see http://groups.yahoo.com/group/RangeVoting
if you want news about what IEVS is finding out)
says MCA is one of the best methods.
3. So here is a new idea intended to take advantage of both ideas.
It is a different-than-usual way to use randomness.
Consider the following randomized variant of the MCA voting method.
Voters rate each candidate either 1, 2, or 3 (3 is best).
The candidate with the most 3-ratings wins if his number of
3-ratings exceeds X% of the number of voters.
Otherwise, the candidate with the most {2- or 3-ratings} wins.
Here X is chosen randomly and is not known to the voters when casting
their votes.
The point is: if X were some fixed known constant (conventional MCA
method: X=50%), then with a huge number of voters,
it would be virtually certain the election would end in the 1st round,
or virtually certain it would end in the 2nd round. The voters
would get wise to which. Once they knew which round it was going to be,
then the election would really just be an approval-voting election,
and any advantages of the 3-slot over regular 2-slot voting, would
essentially not exist.
I think the difference between virtually certain and *guaranteed* can be
important/significant. Election methods in my book shouldn't be assumed to be
of equal merit just because they nearly always (in simulations and/or in
practice) elect the same winner.
Limiting voters to expressing two preference-levels is in my book
unacceptable and three is a big
improvement. Warren, do you prefer Range3 to Approval?
When the voters are informed strategists and/or if they are mainly
concerned that the winner come
from a certain subset of candidates, then all FBC methods have at least
a very strong tendency to
become equivalent to Approval.
To comment on the specific method proposal: it looks crazy to me. The
method no longer meets
3-slot Majority for Solid Coalitions:
35: A
33: BC
32: CB
If X is revealed as 35% or lower, then A wins in the first round.
Or 3-slot Condorcet(Gross):
26: AB
25: B
25: CB
24: DB
If X is revealed as 26% or lower, then A wins in the first round.
A faction that believes their favourite is the FPP winner might have
extra incentive to only put that
candidate in the top slot, but apart from that the main effect of the
change is that voters will have a
greater fear that their Worse will win in the first round so their
incentive to ignore the middle slot
will be increased, making the method (even) more like Approval, not less.
Chris Benham
election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet and Participation, Moulin's proof
Michael Ossipoff wrote: Sure, Condorcet fails Participation. And of course it would be better to not fail Participation. But Partilcipation isn't about a strategy dilemma. It's about an embarrassment. You know that no method can aviod embarrassments of some kind or other. You know, that goes back to Kenneth Arrow. My intention in drawing attention to that proof was to provide ammunition in favour of Condorcet, not against it. Condorcet's Participation failure apparently requires there to be four candidates in a cycle, which I don't consider to be a practical concern. But I use Partilcipation when comparing Approval to IRV. Some say that's dishonest, to use Participation when my favorite method, Condorcet, fails Participation. I would say that it is somewhat misleading and inconsistent, and counter-productive to the goals of educating people and promoting the Condorcet criterion. But it isn't, because, unlike Condorcet, IRV has no redeeming qualities to outweigh its Participation failure. To be charitable, that is an absurd exaggeration made purely for the sake of being provocative. A more intelligent and appropriate attack on IRV could be made along the lines that it's Participation failures are much more severe than Condorcet's because they are possible in relatively common-place scenarios with just three candidates and no cycle. (This seems to be Auros/M.Harman's main objection to IRV.) So it seems to me that some weakened form of the Participation criterion that captures one of IRV's problems versus Condorcet might be of some use/interest. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] SFC
Warren Smith wrote: SFC: If no one falsifies a preference, and there's a CW, and a majority of all the voters prefer the CW to candidate Y, and vote sincerely, then Y shouldn't win. I must say, SFC is then rather silly. It says if no one falsifies a preference redundantly since it also says a majority of all the voters prefer the CW to candidate Y (of course they do, that followed from defn of CW and fact nobody falsified a preference) and redundanty it also says and vote sincerely (of course they do, since nobody falsified a preference) The criterion refers to all sincere preferences, and by falsifies it means order-reverse and not just truncate or otherwise falsely equal-rank. It is about a faction whose favourite Y isn't the sincere CW not being able to elect Y just by truncating. So say sincere is 43: AB 10: BA 10: BC 37: CB B is the CW, so there's a CW. If the A supporters truncate 43: A 10: BA 10: BC 37: CB Now CBAC, but no-one has falsified a preference and more than half the voters (a majority) have voted sincerely expressing their preference for the (sincere) CW(B) over Y (A in this example, BA 57-43), so the criterion says that in this scenario A mustn't win. This isn't the same as the Condorcet criterion, because BP/RP/MM/River(Margins) and Smith/Schwartz,IRV all meet Condorcet but elect A. I speculate that the reason for the confusing unusual language is to do with Mike's long-running propaganda war in favour of Winning Votes and Approval versus Margins and IRV. My stab at making it clearer and more technical: If more than half the voters vote X over Y and it is possible to complete truncated ballots in a way to make X the CW, then Y must not win. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] Condorcet and Participation, Moulin's proof
[EM] Condorcet and Participation *Markus Schulze * [EMAIL PROTECTED] mailto:markus.schulze%40alumni.tu-berlin.de /Sun Oct 5 02:48:02 2003/ * Previous message: [EM] lower preferences http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011029.html * Next message: [EM] (no subject) http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011031.html * *Messages sorted by:* [ date ] http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/date.html#11030 [ thread ] http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/thread.html#11030 [ subject ] http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/subject.html#11030 [ author ] http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/author.html#11030 Dear participants, this is Moulin's proof that participation and Condorcet are incompatible. Situation 1: 3 ADBC 3 ADCB 4 BCAD 5 DBCA Situation 2: Suppose candidate B is elected with positive probability in situation 1. When we add 6 BDAC voters then candidate B must be elected with positive probability according to participation and candidate D must be elected with certainty according to Condorcet. Situation 3: Suppose candidate C is elected with positive probability in situation 1. When we add 8 CBAD voters then candidate C must be elected with positive probability according to participation and candidate B must be elected with certainty according to Condorcet. Situation 4: Suppose candidate D is elected with positive probability in situation 1. When we add 4 DABC voters then candidate D must be elected with positive probability according to participation and candidate A must be elected with certainty according to Condorcet. Situation 5: Because of the considerations in Situation 2-4 we get to the conclusion that candidate A must be elected with certainty in situation 1. When we add 4 CABD voters then candidate B and candidate D must be elected each with zero probability according to participation. Situation 6: Suppose candidate A is elected with positive probability in situation 5. When we add 6 ACBD voters then candidate A must be elected with positive probability according to participation and candidate C must be elected with certainty according to Condorcet. Situation 7: Suppose candidate C is elected with positive probability in situation 5. When we add 4 CBAD voters then candidate C must be elected with positive probability according to participation and candidate B must be elected with certainty according to Condorcet. Markus Schulze * Previous message: [EM] lower preferences http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011029.html * Next message: [EM] (no subject) http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/011031.html * *Messages sorted by:* [ date ] http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/date.html#11030 [ thread ] http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/thread.html#11030 [ subject ] http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/subject.html#11030 [ author ] http://lists.electorama.com/pipermail/election-methods-electorama.com/2003-October/author.html#11030 election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] replies to recent EM posts re voting-design puzzle
Warren Smith wrote:
Benham: Right. And how does a voter express an infinitesimal preference in
the Range 0-99 that you advocate?
--sorry, when I speak of range voting in mathematical analysis, I almost
always mean
continuum range voting where all real numbers in [0,1] are castable votes.
That is convenient for you, but I've also seen the claim made in
propaganda apparently in support of the version/s of Range
you propose as a practical reform.
http://www.rangevoting.org/
1. Each vote MeaningOfVote.html consists of a numerical score
within some range (say 0 to 99 Why99.html) for each candidate.
Simpler is 0 to 9 (single digit range voting). Voters may also
indicate X Blanks.html or NO OPINION Blanks.html if they
have no opinion about a candidate. Such votes don't affect that
candidate's average.
UNAFFECTED BY CANDIDATE CLONING: CandCloning.html Consider the
situation where A has clones A_2 and A_3 . In the old plurality
voting Plurality.html system, the clones split the vote and lose.
In the Borda voting rangeVborda.html system, a party assures
victory merely by running enough clones. In contrast, in Range voting,
A is neither harmed nor helped. No more bitter enmity Enmity.html
between alike candidates
As far as I am concerned, restriction to discrete sets such as {0,1,...,99} is
not really a good idea and is only done for reasons of practicality (interface
with
old voting machines, etc). I therefore prefer it if more and more 9s are
allowed. There is some
reason to believe (in fact, precisely the sort of reason Benham speaks of) that
about six 9s
may be desirable.
I can see how by this trick you achieve Strong FBC and your special
version of Clone Independence (ICC).
Chris Benham
election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] EM] Simmons' solution of voting system design puzzle is inadequate
Warren Smith wrote:
Benham: By this definition Range fails ICC because voters can only express
preferences among clones by not giving maximum possible score to all of
them, thus making it
possible that if a narrow winner is replaced by a set of clones all the
clones lose.
--no. The definition in the problem statement said slight preferences among
clones.
By slight, I meant, to be formal, infinitesimal.
Right. And how does a voter express an infinitesimal preference in
the Range 0-99 that you advocate?
499: A99
251: B99C98
250: C99B98
Range average scores: A49.401,B49.349, C49.348
A wins, but if the {B,C} clone set is coalesced into a single candidate
X, X wins. This is an FPP-like failure of
Clone-Winner, and BTW also of course a failure of Majority for
Solid Coalitions (and Condorcet).
499: A99
501: X99
Range average scores: X49.599,A49.401
Apart from that, I gather that Range with fewer available ratings
slots also qualifies as Range Voting, so
of course in that case it is even more difficult for the voter to
express infinitesimal preferences.
Chris Benham
election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Simmons' solution of voting system design puzzle is inadequate
Abd ul-Rahman Lomax wrote: Abd ul-Rahman Lomax wrote: At 05:00 PM 1/20/2007, Chris Benham wrote: By this definition Range fails ICC because voters can only express preferences among clones by not giving maximum possible score to all of them, thus making it possible that if a narrow winner is replaced by a set of clones all the clones lose. Now, tell me, why should an election system provide a means for voters to express a preference between clones, when they consider them equally fit for the office? Benham is correct that Range would not allow a voter to express a max score to one candidate and a lower score to another, without risking the loss of the second one as he described. If a voter considers two candidates clones, the rational vote under Range is to rate them identically. Favorite, between clones, is meaningless. If the voter has a preference, they aren't clones to the voter. Wrong. That is not how Warren defined clones for his purpose, nor is it how they are regularly defined. *clones* A set of alternatives, X[1], X[2], .. X[m] is a clone set provided that for every alternative Z, where Z is not one of X[1], .. X[m], the following is true: Every ballot that ranks Z higher than one of X[1] .. X[m] ranks Z higher than all of them. Every ballot that ranks Z lower than one of them, ranks Z lower than all of them. No ballot ranks Z equal to any of them. As well, there must be at least one alternative outside the set of clones, and at least two alternatives in the set of clones. So this: Now, tell me, why should an election system provide a means for voters to express a preference between clones, when they consider them equally fit for the office? is more-or-less a contradiction in terms. Okay, so I looked up clone. It has a special meaning; the term was invented to apply to ranked methods. According to the current Wikipedia article on Strategic Nomination: Clones in this context are candidates such that every voter ranks them the same relative to every other candidate, i.e. two clones of each other are never both strictly separated by a third member in the preference ranking of any voter, unless that member is also a fellow clone. Yes. Because of this definition, it is possible that all voters would rank two candidates the same, but would sincerely rate them differently,.. I think you have that the wrong way round. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Simmons' solution of voting system design puzzle is inadequate
Warren Smith wrote: Here is the current CRV web page about this problems and its (lack of) solution We are speaking about puzzle #5 at http://www.rangevoting.org/PuzzlePage.html --- Puzzle #5: Voting systems immune to clones and avoiding favorite-betrayal Puzzle: Two desirable properties of a voting system - both of which Range Voting has - are immunity to candidate-cloning (ICC) and avoiding favorite betrayal (AFB). AFB: voters should never have strategic incentive to betray their favorite candidate by voting him below some other. ICC: political parties should be unable to usefully manipulate an election by running clones of their own, or of an opposed, candidate; voters here are assumed to vote honestly and to have only tiny preferences (which they may express in their votes, if they exist) among the clones. By this definition Range fails ICC because voters can only express preferences among clones by not giving maximum possible score to all of them, thus making it possible that if a narrow winner is replaced by a set of clones all the clones lose. Note: Many voting systems are known (beyond just variants of range voting) which satisfy AFB Many? There is MCA, ER-Bucklin(Whole), one or two Kevin Venzke methods and what else? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Strongest pair with single transfer (method)
Kevin, Interesting. What (if any) harm would be done by applying this to the three candidates remaining after the rest have been IRV-style eliminated? Is there any actual criterion that this method meets but IRV doesn't? Chris Benham Kevin Venzke wrote: Hi, Here's an attempt at a method that behaves well in the three-candidate scenario with preferences based on distance on a one-dimensional spectrum. I would call it strongest pair with single transfer or SPST. It satisfies LNHarm and Plurality, and doesn't suffer from the worst kind of burial incentive. It also satisfies Clone-Loser I believe, though not monotonicity. My idea was to come up with a method that, in the three-candidate case with distance-based preferences on a one-dimensional spectrum, could elect the inner candidate in the absence of a majority favorite. I also wanted to avoid truncation strategy (Approval, Condorcet), gross Plurality failures (as under MMPO), and the sort of burial strategy where you give a lower preference to a candidate whose supporters are not ranking your candidate. Definition: 1. The voter may vote for one first preference and one second preference. 2. The strength of a candidate, or pair of candidates, is defined as the number of voters giving such candidates the top position(s) on their ballots in some order. (This is as under DSC.) 3. A pair of candidates has no strength, if it includes any candidate who is not among the top three on first preferences. (I don't like this rule, but it's needed for LNHarm.) 4. If the strongest candidate is in the strongest pair, or stronger than the strongest pair, then this candidate wins. 5. Eliminate the strongest candidate. The second preferences of his supporters may be transferred to the individual candidate strengths of the two members of the strongest pair of candidates. 6. Now, the strongest candidate in the strongest pair is elected. examples: 40 AB 25 BC 35 CB Strongest pair is BC; strongest candidate is A. BC is stronger than A, so A is eliminated and 40 preferences are transferred to B's strength. B wins. 35 AB 25 BC 40 CB Here BC is again the strongest pair, but C is the strongest candidate and wins immediately unfortunately. This method is a lot like DSC, but never requires more than N^2 numbers to be counted, whereas DSC requires 2^N if you keep track of every set. The elimination doesn't create IRV's counting issues, since with only two preferences taken we can just count them all. The burial strategy works like this: Say it's A, B, and C, with B as the middle candidate. A is expected to be the strongest candidate. Then voters with the preference order BA have incentive to instead vote BC. This is because if BC is the strongest pair, A will be eliminated and hopefully transfer preferences to B. But if AB is the strongest pair, A wins outright. As a result of this strategy, it is possible that (despite the LNHarm guarantee) A voters would decline to give a second preference to B, so that BA voters can't count on the A voters to give a second preference to B. It is only possible to eliminate the first preference winner, due to LNHarm. It's only safe to eliminate a candidate who was going to win. Otherwise it could happen that voters have incentive to weaken a pair involving their favorite candidate, in order to prevent an elimination that causes the favorite candidate to lose to the second preference. Limiting pairs to the top three FPP candidates is necessary for LNHarm when there are more than three candidates. Otherwise it could happen, say, that BC is stronger than BD is stronger than A, A is eliminated, and then C wins. Whereas if BC were weakened and BD were strongest, A's elimination might result in B winning. Monotonicity can be failed when the winner is not the FPP winner, he gets more preferences, changing which pair is strongest, and causing the other candidate in the pair to win. I ran some simulations to try to measure this method against others. When the only ballot types are AB, BA, BC, and CB, this method is identical to DSC. When all 9 ballot types are allowed, this method seems to be strictly more Condorcet-efficient than DSC, although not by much. I found that IRV is more Condorcet-efficient than either, except in the scenario where only the four ballot types are permitted, and the proportions of the BA and BC ballots are divided by 5. There IRV is worse because it wants to eliminate B. (With the four ballot types, IRV can elect B as long as B doesn't have the fewest first preferences. That particular scenario is important to me, though. DSC can elect B unless, say, the AB faction outnumbers the BA BC factions, and also the BC CB factions.) That's it for now. Kevin Venzke ___ Découvrez une nouvelle façon d'obtenir des réponses à toutes vos questions ! Profitez des connaissances, des opinions et des expériences des
Re: [EM] New 3-slot FBC method (not)
Oops! Some on this list might know to be sceptical when I suggest a new method meets FBC. 37: WF 25: FC 07: C (sincere is FC) 31: CW Approvals: W68, C63, F62. Top-rating scores: C38, W37, F 25. Winning threshold T =50. No candidate has a TR score equal or above the threshold, so the least approved candidate F is eliminated and then on the 25FC ballots C is promoted to top rating, boosting C's TR score to 56, above T so C wins. But if the 7C voters stop betraying their sincere favourite and change to C=F, we get: 37: WF 25: FC 07: C=F 31: CW Approvals: F69, W68, C63. Top-rating scores: C38, W37, F 32. Winning threshold T =50. This has the effect of boosting F's approval score so now C is eliminated and W is promoted to top rating on the 31CW ballots so giving W a winning score. So this method clearly fails FBC. I withdraw my support for this method because I don't like single-winner methods that fail Independence from Irrelevant Ballots (IIB) without meeting FBC. Sorry about that, Chris Benham Chris Benham wrote: I have an idea for a new 3-slot method, and if people like it I'm open to suggestions for a name. (It is similar to and partly inspired by Douglas Woodall's ApAV method.) 1. Voters give each candidate a top rating , a middle rating or no rating. 2. Fix the winning threshold T at 50% of the total valid ballots. Give each candidate a score equal to the number of ballots on which it is top-rated. If the candidate X with the highest score has a score equal or greater than T, elect X. 3. If not, eliminate the (remaining) candidate which is given a top or middle rating on the fewest ballots, and on ballots that now top-rate none of the remaining candidates promote all the middle-rated candidates to top-rated and accordingly amend the scores. 4. Again, if the now highest scoring candidate X has a score of at least T then elect X. (T does not shrink as ballots 'exhaust'). 5. Repeat steps 3 and 4 until there is a winner. If no candidate ever reaches a score of T, elect the candidate that is top or middle rated on the most ballots (i.e. the Approval winner). Note that in the course of the count no candidates are ever demoted on any ballots from middle-rated to unrated. Both the winning threshold and the elimination order is fixed at the start and don't change. election-methods mailing list - see http://electorama.com/em for list info
[EM] New 3-slot FBC method
I have an idea for a new 3-slot method, and if people like it I'm open to suggestions for a name. (It is similar to and partly inspired by Douglas Woodall's ApAV method.) 1. Voters give each candidate a top rating , a middle rating or no rating. 2. Fix the winning threshold T at 50% of the total valid ballots. Give each candidate a score equal to the number of ballots on which it is top-rated. If the candidate X with the highest score has a score equal or greater than T, elect X. 3. If not, eliminate the (remaining) candidate which is given a top or middle rating on the fewest ballots, and on ballots that now top-rate none of the remaining candidates promote all the middle-rated candidates to top-rated and accordingly amend the scores. 4. Again, if the now highest scoring candidate X has a score of at least T then elect X. (T does not shrink as ballots 'exhaust'). 5. Repeat steps 3 and 4 until there is a winner. If no candidate ever reaches a score of T, elect the candidate that is top or middle rated on the most ballots (i.e. the Approval winner). Note that in the course of the count no candidates are ever demoted on any ballots from middle-rated to unrated. Both the winning threshold and the elimination order is fixed at the start and don't change. I think this is now my favourite method that meets FBC/SF. I have it meeting this and Mono-raise and 3-slot Majority for Solid Coalitions, and Plurality and Minimal Defense. Comparing it with MCA and ER-Bucklin(Whole) it seems to have a less severe LNHarm problem and no disadvantages that I can see except that is slightly more complicated than MCA. Also it has several advantages over Majoritarian Top Ratings(MTR). It doesn't have as bad a Clone-Winner problem. 25: AB 23: BA 45: C 07: D MTR elects C here while my suggested method (majoritarian disapproval elimination? MDE) elects A. B is a clone of A, and if B is dropped from the ballots then both methods elect A. MDE probably fails Condorcet(Gross), but doesn't as easily fail Condorcet Loser. 5:AB 5:BC 5:CA 3:DA 3:DB 3:DC Here MTR elects the Condorcet Loser and Approval Loser D. I think MDE can only elect a Condorcet loser who is the Approval winner. Also in MTR zero-info. voters with one big sincere ratings gap (so they are chiefly concerned that any one of the acceptable/good candidates defeats all the unacceptable/bad candidates) have the weird incentive to randomly middle-rate half the unacceptable candidates in the hope of artificially handing out some majority-strength defeats. In MDE those voters should simply not middle-rate any of the candidates (certainly none of the Unacceptables). MTR has a saleability problem in that it uses a pairwise mechanism as part of its algorithm (MDD), but then fails both Condorcet and Condorcet Loser . I think MDE's algorithm is more natural and more appealing to say IRV supporters. I'm interested in any comments or corrections. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Clone proofing Copeland
Juho, 26: AB 25: CA 49: BC (sincere is BA or B) Juho wrote: But I'll however mention some random observations that the example that you used made me think. - One could also claim that these votes are a result of strategic voting but in another way than what you described. Instead of having 49 voters that strategically changed their vote from BA (or B) to BC one could have had just one voter that strategically changed her vote from CA to AB. As a result numbers 25 and 26 were swapped and counting the first place votes gives a different result. The strategic voter was not able to get her #1 favourite but she could easily help her #2 favourite become elected. Yes, but that is just an instance of vulnerability to the Compromise strategy common to all methods that meet Majority for Solid Coalitions. The Achilles' heel of Condorcet methods in their competition with IRV is their vulnerability to Burial. - In addition to strategies one of course also has to pay attention to the sincere votes. What would be the best candidate to elect if the votes in the example were all sincere? Arguably maybe B, but also arguably without rating information we can't tell. There is thus always a balance on how much one needs to protect against strategic voters since all such changes in the methods (in most cases) make the achieved utility with sincere votes a bit worse. I think DMC strikes a good balance. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Clone proofing Copeland
Simmons, Forest wrote: Here's a version that is both clone proof and monotonic: The winner is the alternative A with the smallest number of ballots on which alternatives that beat A pairwise are ranked in first place. [shared first place slots are counted fractionally] That's it. This method satisfies the Smith Criterion, Monotonicity, and Clone Independence. More not-so-good news for this Simmons method: it fails mono-raise (aka Monotonicity). 31: AB 02: AC 32: BC 35: CA CABC. Simmons scores: A35, B33, C32. C has the lowest score and wins. But if we raise C on the two AC ballots, changing them to CA, then we get: 31: AB 32: BC 37: CA (2 of these were AC) CABC. Simmons scores: A37, B31, C32. Now B has the lowest score and wins. So raising C on some ballots without changing the relative ranking of any of the other candidates has caused C to lose, a failure of mono-raise. Interestingly in both cases the method gave the same result as IRV. In fact it is starting to look as though in the 3-candidate case Schwartz//Simmons is equivalent to Schwartz,IRV! Say sincere is: 48: A 27: BA 25: CB B is the CW, and in this case both methods (even without the Schwartz component) elect B. And both methods are vulnerable to the same Pushover strategy. If from 3 to 20 of the 48 A supporters change their vote to CA or C or even CB, then both methods will elect A. 45: A 03: CA (sincere is A) 27: BA 25: CB BACB Simmons scores: A27, B28, C45. A has the lowest score and so wins. IRV eliminates B and likewise elects A. 28: A 27: BA 45: CB (20 of these are sincere A!) BACB Simmons scores: A27, B45, C28. A has the lowest score and so wins. IRV eliminates B and likewise elects A. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Clone proofing Copeland
Juho wrote: How about the smallest number of ballots on which some alternative that beats A pairwise is ranked higher than A? Juho No, that would have nothing like the same strength or resistance to Burial. 26: AB 25: CA 49: BC (sincere is BA or B) The Simmons method narrowly elects A (the sincere CW), while your suggestion easily elects the Burier's candidate B. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Simmons cloneproof method is not cloneproof
Warren Smith wrote: see http://groups.yahoo.com/group/RangeVoting/message/2934 for counterexample (plus linear program explainign how I found the counterexample) wds Ballots: 6: ABC 3: CAB 4: BCA A wins under Simmons voting since A beats B pairwise == 6 ballots count against B C beats A pairwise == 3 ballots count against A B beats C pairwise == 4 ballots count against C Now add two clones of A in a Condorcet cycle. Then A1 is beat pairwise by A2 with 1/3 of the 6 of the A-top ballots, i.e. 3, and ditto A2 and A3, all have 2 A-top ballots against them. Plus, all the Ak have got C's toprank votes against them, which is 3. So in total, each A-clone has 5 ballots against it, while C has only 4 ballots against it. Hence C is now the winner thanks to A's cloning. So SIMMONS IS NOT CLONEPROOF!! If we agree only to clone non-winners, or if, when cloning a winner, all voters agree to rank the clones EQUALLY, THEN Simmons is cloneproof. Proof: After cloning, the A-beats-B relations are unaffected under these constraints, and the number of top-rank-votes-against X are either unaltered - or increased (increase is only possible for nonwinner X since winning-X clones never pairwise-beat each other). QED However... this weakened kind of cloneproofness is a good deal less impressive than genuine cloneproofness. So Simmons meets Clone-Loser, but can fail Clone-Winner when there are three or more factions in a top cycle and the candidates in one of those factions are in a sub-cycle. That is a very very mild failure of Clone-Independence and arguably not a practical worry. If that is the full extent of the bad news (and maybe even if it isn't) then I think this method remains a great contender (for best practical Condorcet method) because of its tremendous Burial resistance and simplicity. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Clone proofing Copeland
Simmons, Forest wrote: Here's a version that is both clone proof and monotonic: The winner is the alternative A with the smallest number of ballots on which alternatives that beat A pairwise are ranked in first place. [shared first place slots are counted fractionally] That's it. This method satisfies the Smith Criterion, Monotonicity, and Clone Independence. Warren Smith wrote: this is an elegant method! Note that it is IMMUNE to my DH3 pathology! http://rangevoting.org/DH3.html It is strategically pointless to bury (lower artificially) a rival to your favorite below some non-entities, because if those nonentitites are never ranked top, doing so makes no difference. And it satisfies mono-add-plump and mono-append (two Woodall criteria)! And it is simple! Assuming these criterion compliance claims are right , so far I am very very impressed. Congratulations Forest! It seems to completely dominate Schwartz,IRV which until now was one of my favourite Condorcet methods. I am convinced that it has an anti-burial property stronger than I suspected it was a possible for an unadorned Condorcet method to have. One of the reasons I liked Schwartz,IRV was that it met what I called Dominant Mutual Third Burial Resistance, a criterion that said that if there are three candidates X,Y,Z and X wins, then changing some ballots from YX to YZ can't make Y the winner. Well I'm quite sure this Simmons method meets Dominant Mutual *Quarter* Burial Resistance! 26: AB 25: CA 49: BC (sincere is BA or B) ABCA. Simmons scores: A25, B26, C49. A has the lowest score and so narrowly wins. On top of that it has the advantage over Schwartz,IRV of meeting mono-raise (and so isn't vulnerable to Pushover strategy), and doesn't seem to have any disadvantage. It definitely fails two of Steve Eppley's criteria: Minimal Defense and Truncation Resistance (not ones I rate highly). /truncation resistance/ Proof%20MAM%20satisfies%20Minimal%20Defense%20and%20Truncation%20Resistance.htm: Define the sincere top set as the smallest subset / / of alternatives such that, for each alternative in the subset, say /x/, and / / each alternative outside the subset, say /y/, the number of voters who / / sincerely prefer /x/ over /y/ exceeds the number who sincerely prefer /y/ over /x/. If no voter votes the reverse of any sincere preference regarding any pair of alternatives, and more than half of the voters rank some /x/ in the sincere top set over some /y/ outside the sincere top set, then /y/ must not be elected. (This is a strengthening of a criterion having the same name promoted by Mike Ossipoff, whose weaker version applies only when the sincere top set contains only one alternative, a Condorcet winner.)/ / I'm not sure about his Non-Drastic Defense criterion, (the version) that says that if Y is ranked no lower than equal-top on more than half the ballots and Y pairwise beats X, then X can't win. It has Woodall's Symmetric Completion property, and it certainly meets his Plurality criterion when there are three candidates (and probably meets it period). I'm happy with its performance in this old example: 101: A 001: BA 101: CB It easily elects A. Schulze (like the other Winning Votes defeat dropper methods) elects B. It meets my No Zero-Information Strategy criterion, which means that the voter with no idea how others will vote does best to simply rank sincerely. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] RE : Re: Election methods in student government...
Tim Hull wrote:
DSC uses a somewhat interesting method - it effectively goes and
excludes the groups of candidates that the most people prefer a solid
coalition to until it finds a winner. However, what I am wondering
is - what are the primary flaws of these two methods (especially as
compared with IRV, of which I know quite a bit about the flaws)?
DSC fails several important (in my book) criteria that are met by IRV.
DSC fails Dominant Mutual Third, which says that if there is a set of
candidates X that all pairwise beat all the outside-the-set candidates
and they are solidly supported
(ranked above all the outside-the-set candidates) on more than a third
of the ballots, then the winner must come from X.
49: A
48: B
03: CB
Here the DMT set is {B}, but DSC elects A.
(If the B voters switch to BC then B wins, a failure of Later-no-Help.)
DSC fails Condorcet Loser, which says that a candidate that is
pairwise beaten by every other candidate mustn't win
38: A
19: BCD
17: BDC
10: CB
03: CD
10: DC
03: DB
DSC fails Condorcet Loser by electing A.
This is also a failure of Dominant Mutual Third (DMT), by not electing B.
IRV is invulnerable to the Burying strategy.
49: A
48: BA
03: CB
DSC elects A, but if the BA voters change to BC then their burial
strategy against A succeeds and B wins.
DSC has a random-fill incentive and so fails what I call No
Zero-Information Strategy. In the 0-info. case the DSC voter
gets a better expectation by strictly ranking all the candidates, if
necessary at random; whereas the IRV voter does best to
rank sincerely.
I think of DSC as just FPP that has been minimally improved to meet
Clone-Winner and Majority for Solid Coalitions.
Chris Benham
election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] RE : Re: Election methods in student government...
Chris Benham wrote:
38: A
19: BCD
17: BDC
10: CB
03: CD
10: DC
03: DB
My example here of DSC failing both DMT and Condorcet Loser works, but
not quite what I meant to type:
38: A
19: BCD
17: BDC
10: CD
03: CB
10: DC
03: DB
(I've corrected it below as well).
Chris Benham
Tim Hull wrote:
DSC uses a somewhat interesting method - it effectively goes and
excludes the groups of candidates that the most people prefer a
solid coalition to until it finds a winner. However, what I am
wondering is - what are the primary flaws of these two methods
(especially as compared with IRV, of which I know quite a bit about
the flaws)?
DSC fails several important (in my book) criteria that are met by IRV.
DSC fails Dominant Mutual Third, which says that if there is a set
of candidates X that all pairwise beat all the outside-the-set
candidates and they are solidly supported
(ranked above all the outside-the-set candidates) on more than a third
of the ballots, then the winner must come from X.
49: A
48: B
03: CB
Here the DMT set is {B}, but DSC elects A.
(If the B voters switch to BC then B wins, a failure of
Later-no-Help.)
DSC fails Condorcet Loser, which says that a candidate that is
pairwise beaten by every other candidate mustn't win
38: A
19: BCD
17: BDC
10: CD
03: CB
10: DC
03: DB
DSC fails Condorcet Loser by electing A.
This is also a failure of Dominant Mutual Third (DMT), by not
electing B.
IRV is invulnerable to the Burying strategy.
49: A
48: BA
03: CB
DSC elects A, but if the BA voters change to BC then their burial
strategy against A succeeds and B wins.
DSC has a random-fill incentive and so fails what I call No
Zero-Information Strategy. In the 0-info. case the DSC voter
gets a better expectation by strictly ranking all the candidates, if
necessary at random; whereas the IRV voter does best to
rank sincerely.
I think of DSC as just FPP that has been minimally improved to meet
Clone-Winner and Majority for Solid Coalitions.
Chris Benham
election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] majoritarian top ratings (MTR)
Kevin Venzke wrote:
Hello,
My favorite method lately I'll call majoritarian top ratings or MTR.
I don't believe it has been suggested on the list. Here is the definition:
1. The voter gives every candidate the top rating, the middle rating,
or no rating at all, which is the bottom rating.
2. Say that a candidate X is defeated by a majority if more than half
of all voters assign some other candidate Y a strictly higher ranking
than they assign to X.
3. Elect the top candidate in the ordering of candidates wherein a
candidate X is above candidate Y when X is not defeated by a majority
while Y is, or (when this makes no distinction) when X received the top
rating on more ballots than did Y.
Kevin,
Is there some reason apart from simplicity that you use MDD instead of
CDTT?
5:AB
5:BC
5:CA
3:DA
3:DB
3:DC
All except D has a majority-strength defeat, but D is pairwise beaten
10-9 by every other
candidate.
CDTT can't be just the Condorcet loser, as the MDD set is here.
Advantages of this:
1. FBC
2. (my interpretation of) minimal defense
3. limited later-no-harm, in that you can't hurt your top-rated candidates
by listing middle-rated candidates.
I suppose you can add the 3-slot versions of Smith(Gross) and
Majority for Solid Coalitions.
Disadvantages:
1. fails Plurality (although not as egregiously as MMPO)
2. potential for burial strategy (although with the usual countermeasures)
Take the 0-info. voters whose main or only preference is between candidates
they regard as acceptable and all the others they regard as unacceptable
(i.e. they have one big gap in their sincere ratings). For them the sincere
way of voting would be to ignore the middle slot and just submit an approval
vote, putting all the unacceptables in the bottom slot.
But in fact their best strategy is to randomly select half the unacceptables
and put them in the middle slot, maybe causing one that would otherwise beat
an acceptable candidate to be disqualified.
With information, the middle slot would mainly become a cynical strategy-tool
for factions to try to disqualify the most electible candidate/s in rival
faction/s. The effect of that could be the election of a turkey with little
sincere support.
MTR of course fails Independence from Irrelevant Ballots (IIB), and also
Clone-Winner (unless the defence but these are ratings ballots, and a set of
clones must by definition share the same rating is invoked).
25: AB
23: BA
45: C
07: D
C wins, but if the irrelevant 7D ballots are removed then A wins.
If instead one of the {A,B} clones are removed then the other will win (i.e.
if
the clone-set is replaced by a single candidate X which is top-rated by all
those
who voted AB or BA, then X will win).
It seems to me that FBC/SF compliance is just so expensive and to me
uninspiring
and negative minded. My favourite 3-slot method definitely remains 3-slot
DMC.
FBC complying methods generally at least verge on being strategically equivalent
to plain Approval (in the case of MTR, with extra burial opportunities and a
random-fill
incentive).
Chris Benham
election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Election methods in student government...
Tim Hull wrote: So far, all I have came up with which seems to potentially be a good method is a variant of sequential proportional approval voting. Under the system, single winner elections would be simple approval voting. However, for multi-winner elections each student would begin with a set number of points equal to the number of seats to be elected. Votes would be counted as in normal SPAV, and each weighted according to the number of points each student has remaining. Every time a voter elects one of their choices, they would use up one of their points. This seems a little more understandable than standard SPAV, and it hurts groups that share some preferences with the majority less. Tim, Your gives voters a very big incentive to not vote for someone who they believe will win anyway. In the extreme case there could be a very popular candidate X that fails to be elected because everyone knew that X would win the first seat, so didn't vote for X to avoid losing (using up) a point. Take this election for 4 seats. 11: ABCD 05: D 09: EF By my calculations with your suggested method, it elects DEAF. The ABC faction erred by approving D. 11: ABC 05: D 09: EF Now the winners are AEBF. That isn't a proportional or fair result. D has a Droop Quota and should be elected (or squeezed out in a tiebreaker, but here the EF list easily wins the last seat). The winners should be D, two from ABC and one from EF. For a good single-winner method, I suggest DMC(Ranking). Voters rank candidates they approve, equal-ranking allowed. Elect the Condorcet winner if there is one. Otherwise eliminate the least-approved candidate until one of the remaining candidates X is pairwise undefeated by any of the other remaining candidates. Elect the first X to appear. I also very much like the full version of DMC (that allows voters to rank among unapproved candidates by entering an approval cutoff/threshold). Even 3-slot DMC that uses a 3-slot ratings ballot, top two slots interpreted as approval and default placement in bottom slot, is in my opinion better than Approval or any other 3-slot method. http://wiki.electorama.com/wiki/DMC I might have some PR suggestions in a later message. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] reply to Juho Laatu on range voting
Warren Smith wrote: First: A theorem ( http://rangevoting.org/AppCW.html ) indicates that range and approval voting both return the honest-voter Condorcet winner if all voters act strategically. Basically, if we are not in the prettiest cloud but rather in the I love/hate Nixon emotional mode, then we vote max or min on Nixon. Assuming all voters do that with their threshold placed somewhere between the two candidates they judge as most likely to win, (which they do because they are not strategic idiots) and assuming one of these two happens to be the honest-voter Condorcet winner, then theorem: Range Approval both will elect the honest-voter Condorcet winner, but meanwhile Condorcet methods often will fail to do so. [Juho Laatu claims misleadingly that RV may still elect the Condorcet winner with quite good probability (but only with probability). Actually, under these assumptions, the probability is 1. Further, Condorcet methods with strategic voters will elect the honest-CW with merely a probability strictly below 1.] I can't see that this set of assumptions is really that much different from those needed to say that FPP will certainly elect the sincere CW. [And I can't see anything remotely misleading about Juho's statement]. Second: The claim that honest Range Voters can have their votes outweighed by large factors by strategic ones, is correct. However, (1) at least their honest vote will never actually work against them (e.g. compared to not voting at all) The chance of that happening in practice is very small, I'd say insignificant if the Condorcet method meets mono-raise (like Schulze and DMC and most others). Those methods also allow equal-ranking at the top, so voters in fear of being bitten by Participation failure can avoid it by submitting approval votes. (2) their honest statement X is my favorite in their vote, will never hurt them. You mean their honest statement X is *one* of my favourites (plural) will never hurt them (assuming you mean hurt them in comparison to some other way of voting). ..consider a Condorcet election. Gore loses to Bush thanks to a Nader spoiler effect. The Nader voters complain the voting system penalized us for honestly ordering Nader top, Gore second. If we had had range voting we could have expressed our honest ordering, without being penalized. If the election is close enough in comparison to the number of available slots on the range ballot, then the Nader voters can of course still be penalised for honestly ordering Nader top, Gore second. Second: The claim that honest Range Voters can have their votes outweighed by large factors by strategic ones, is correct. However,.. Anyhow such outweighing (b) is entirely their own fault and hence is self-correcting over time and not a valid attack on the voting system. I reject the idea that voting honestly is a fault. The voting system should try to minimise the advantage of strategists over sincere voters, and of informed strategists over less well informed and zero-info. strategists. It should give the voter a clear way of voting sincerely, and if there is a zero-info. strategy it should be straight-forward and similar to sincere voting. A minimum standard is that the voting method should give good results in the zero-info. case with strategic voters. Say sincere ratings are: 48: A10B4C0 47: B10C6A0 04: C10B4A0 B is the Condorcet and big sincere ratings winner, but if these voters all use the best 0-info. Range/Approval strategy C the sincere ratings loser (SU worst) wins. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Scott Ritchie's FAVS criterion - uniquely favors range voting
Warren Smith wrote: Yes to Chris Benham; I independently came up with a very similar IRV FAVS-violation example and posted it on http://groups.yahoo.com/group/RangeVoting/message/2716 http://groups.yahoo.com/group/RangeVoting/message/2708 To Scott Ritchie, yes, I just invented the name FAVS and IFAVS (incomplete info version). Perhaps FAVA is better name than FAVS. N.Tideman told me, however, that he does not consider FAVS-satisfaction necessarily to be a good thing. In fact, he thinks it is probably a bad thing. So what is that is supposed to be good about satisfying FAVS ? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Scott Ritchie's FAVS criterion - uniquely favors range voting
Warren Smith wrote: About Scott Ritchie's feel alike vote same FAVS criterion that all members of a feel-alike group should want to vote the same. FAVS is falsified by IRV if incomplete information: either A or B need 5 more votes to surpass the hated C and/or the 50% mark (but you do not know which) and your group has 10 votes. So split them. I am not sure whether FAVS is satisfied by IRV in complete information scenarios. I don't know why you are not sure, because I pointed out in my last post that methods like IRV that are vulnerable to Pushover strategy fail this FAVS criterion. Suppose these are the known voting intentions: 48: A 27: BA 25: CB On these votes, IRV eliminates C and elects B. The 48A supporters can do nothing to elect A if they all vote uniformly (because if they give their first preference to A any second preferences won't be counted and obviously if they all give their first preference to B or C then they will simply elect whichever one it is), but if from 3 to 20 of them change their first preference vote to C then B will be eliminated and elect A. 45: A 03: CA (or C, or CB; sincere is A) 27: BA 25: CB Apart from just offending mathematical elegance, this vulnerability to Pushover strategy is the reason why I care about methods failing mono-raise. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Is there a criterion for identical voters casting identical ballots?
Scott Ritchie wrote: I was thinking about corporate elections today, and how under some voting systems an individual would want to strategically vote by submitting multiple, different ballots. I soon realized that this was generalizable to multiple voters with identical preferences in any election. Basically, something like If a group of voters share the same preferences, then their optimal strategy should be to vote in exactly the same way. Scott, Are you referring to 0-info. strategy, or to informed strategy? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Is there a criterion for identical voters casting identical ballots?
Scott Ritchie wrote: On Wed, 2006-12-13 at 21:06 +1030, Chris Benham wrote: Scott Ritchie wrote: I was thinking about corporate elections today, and how under some voting systems an individual would want to strategically vote by submitting multiple, different ballots. I soon realized that this was generalizable to multiple voters with identical preferences in any election. Basically, something like If a group of voters share the same preferences, then their optimal strategy should be to vote in exactly the same way. Scott, Are you referring to 0-info. strategy, or to informed strategy? Chris Benham Good point. STV is only violated with informed strategy, I think (though I may be wrong), while SNTV may be violated with 0 info. Does size of the electorate and of my group count as information for our purposes, or is information just the preferences of other voters? Our purposes? This criterion is *your* idea! :) But if it refers to informed strategy, I don't see the point of limiting the type of information. Maybe you can have more than one version of the criterion, varying according to to the amount and type of information this group of voters has. Assuming this faction is perfectly informed and coordinated, methods like IRV that fail mono-raise and are vulnerable to the Pushover strategy certainly fail this criterion. Also Approval Margins Sort(AMS) aka Approval-Sorted Margins fails it. http://wiki.electorama.com/wiki/Approval_Sorted_Margins Suppose the voting intentions are: 44: A|B 46: B| 07: C|A 03: CB| AMS is a Condorcet method that uses ranked ballots with approval cutoffs (signified by | ). On these votes A is the CW and wins. Assuming that only the 46 B voters are informed and strategy minded, what can they do to make B win the election? If they all vote the same way they can't elect B, but if 30 of them vote BC| and the other 16 vote B|C, then B wins. 44: A|B 16: B|C 30: BC| 07: C|A 03: CB| Now the approval order is B49, A44, C40. AB and CA. The approval margin between A,C (4) is smaller that that between B,A(5) so the first correction to our order of candidates is for A and C to swap positions to give B49, C40, A44. This order is now in harmony with the pairwise defeats (BCA) so B wins. If instead the 46B supporters had all voted B|C then A would have won, and if they'd all voted BC| C would have won. Note that this strategising couldn't have worked with DMC (my favourite in this genre) because it has an anti-burial property (I call Approval Dominant Mutual Third Burial Resistance) that says that if there are three candidates XYZ, and X wins and is exclusively approved on more than a third of the ballots, then changing some ballots from YX to YZ can't change the winner to Y. http://wiki.electorama.com/wiki/Definite_Majority_Choice Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Sainte-Lague, part 3
MIKE OSSIPOFF wrote: The very first use of the Presidential Veto was when George Washington vetoed a bill to apportion the house by LR/Hamilton. We used d'Hondt/Jefferson for a while. There was later another bill to enact LR/Hamilton. It passed and wasn't vetored, and LR/Hamilton was used for a while--till someone pointed out the bizarre paradoxes that it's subject to: Some people move from another state to your state, causing your state to lose a seat. Mike, Can you (or anyone) explain or give a demonstration of how this LR/Hamilton apportionment method could do that? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Range Voting Strategy
Warren Smith wrote: Kevin Venzke posted some news about range voting strategy. I have now written considerably more extensive simulator than his (but inspired by his) and the results are interesting. Somewhat contrary to what Venzke seemed to be concluding, my conclusion is that honest range voting (scaled so you score the best candiate the max, the worst the min, and the rest linearly interpolated) is an impressively good voting strategy in the random voter zero info statistical setting. http://rangevoting.org/RVstrat3.html wds C. Scaled sincerity. Voter linearly transforms utilities to make best have rescaled utility 1, worst 0, and rest linearly interpolated, then uses that as her vote E Mean-based thresholding. The voter gives max to every candidate at least as good as the average value of all candidates, and gives min to the others This doesn't surprise me very much. How does the number of slots on the ratings ballot (the granularity of the Range ballot) affect this? Since E is the best strategy with more than about 10 voters, and with Approval these two strategies are the same, does that mean that from this point of view the fewer the better? Then is Half-Approval (Range 3) better in this respect than Range 100? One slightly interesting approval strategy you didn't list: approve all candidates preferred to all the candidates below the biggest sincere ratings gap between any two consecutively ranked candidates. I think it takes more than three candidates for this to differ from E. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Majority Criterion, hidden contradictions
Abd ul-Rahman Lomax wrote: If a method allows voters to express a strict preference, and Approval does, but it also allows voters to do something else, does this mean that voters who *have* expressed a strict preference, in the manner that the election method permits, are to be considered as not having expressed this preference merely because the method did not allow them to take the alternate path without expressing a strict preference? Typically completely stupid question. How can a voter express a strict preference in Approval. Is there a means to do it? That voters may do something else, which is express a group preference *is irrelevant*. Or is it relevant? How? Suppose we have a lot of hampers of food to give away. We have larger ones that contain more than one type of food, and smaller ones that contain only one type. We then invite recipients to each choose one only hamper to take home. So yes, some of these people could have expressed a strict preference for a certain type of food and a few might have, but we never asked them to and those that did paid the price of getting less food. What in the criterion covers this contingency? For especially obtuse morons, it comes under the heading of criteria that apply to ranked ballot methods. Approval isn't a ranked ballot method, so we ask if the voters each have a candidate they mean to rank alone in first place on a ranked ballot, can we (reasonably, reliably, consistently) infer from the ballots they submit who those candidates are? The answer for FPP is obviously Yes. For this purpose an FPP ballot can properly be considered to be simply a ranked ballot that doesn't allow equal-ranking at the top. The fact that the lower preferences are ignored or invisible or don't exist is irrelevant. I'm not sure that Benham said exactly what he intended to say.. I did. I'm normally careful to do that. We assume that voters intend to do what they did. For criteria that apply to ranked ballots, we assume that the voters mean to submit a ranked ballot. Venzke and Woodall interpret Approval ballots as ranked ballots with all the ranked candidates approved and the numbers indicating the order in which they are ranked obscured. I think Abd's real-world propaganda concerns are misplaced. In situations where FPP elects a majority winner, supporters of that candidate will usually have enough pre-poll information to know to use the exclusively approve your favourite strategy. In fact usually it will be known in advance who the two front-runners are, and if the voters in general adopt the sensible approve the front-runner I prefer to the other plus all the candidates I prefer to both of them strategy then of course in practice Approval will always elect a majority favourite. Approval is in much bigger trouble in comparison to IRV, which *does* have it all over Approval in terms of majority-related guarantees (except perhaps for Minimal Defense). Promoting Approval versus IRV requires continually hammering Favourite Betrayal Criterion, ultimate simplicity and huge bang for buck, and Minimal Defense. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] RE : Re: RE : Majority Criterion, hidden contradictions
Abd ul-Rahman Lomax wrote: No, Range does this. If we assume that voters express their expected value for the various candidates, the expected value for the voters, collectively, is the sum of the individual expectations. Sure, but I don't see how this assumption can be taken for granted. No election method can extract information from the voters and use it to determine the winner if the voters do not express the information. The assumption cannot be taken for granted, which is exactly why I expressed it as an assumption. However, what is being said is that if people use Range sincerely and honestly, Range will maximize expected value, summed over all the voters. Yes, but how many of "the people"? 90: A9B1 (sincere is A9B1) 10: B99A0 (sincere is B5A3) All the voters have a sincere low opinion of both candidates, but 90% think that A is 900% better than B and yet B wins (with only 10% of the voters not being "sincere and honest"). Consider a diagnostic tool, a questionnaire to be filled out to determine health status and medical treatment. If people lie on the questionnaire, the results will be suboptimum. Now, the question then becomes, will people lie? Some will, depends on the definition of "lie." The definition is fuzzy because the voters are not even being asked a clear unambiguous question. Here is the paradox: if voters care little about whether or not A or B wins, but want A to win, they can distort the rating of B. For the condition to be true, the voters must simultaneously "care little" and care enough to lie about their true preferences. That rests on the false assumption that it is (significantly) more bother to lie than to tell the truth. In fact it seems to me to be less bother. I can well imagine being sure that I prefer A to B but not sure exactly what my honest rating of each is, so I'd find it easier to vote A max. and B min. My real point is that we don't know, very well, how voters will actually behave. We very much need real-world examples, theory will only take us so far. If we can't make this assumption then there is no guarantee that Range will outperform a majoritarian method in terms of expected value. We can certainly be sure majoritarian methods will outperform Range in the worst-case scenarios. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] RE : Ranked Preference benefits
l the candidates are in the initial DM set, so C is eliminated and then
the "new DM set" is {R} so R wins.
Example 4. Some of the large party voters think C is good but
majority of them think C is no good.
15: LCR
30: LCR
14: RCL
26: RCL
15: CL=R
Initial approvals: L45, C44, R40
CR, CL, LR, so initial DM set is {L,C}.
Initial top preferences: L45, R40, C15.
C is eliminated and L wins (agreeing with your method).
Chris Benham
election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] RE : Ranked Preference benefits
Juho, You mentioned strongest indicated preference gap as the approval cut. How about defining it dynamically so that one would find the strongest preference relation that still has non-eliminated candidates at both sides of it? (like in RP) CB: I did. Or if I didn't make it clear, I meant to. Otherwise there wouldn't be any point to the lower ranked preference gaps. Interpreting ballots as approving all candidates above the strongest indicated preference gap... Recalculate (among remaining candidates) the DM set and repeat the whole process until an X is elected. When we repeat the whole process, strongest indicated preference gap refers to preference gap among remaining candidates. BTW, the initials RP are well taken by Ranked Pairs so if your method is going to stick around maybe it should have a different name. The name ranked preferences seems to just refer to the ballot style, which has been previously on EM called a dyadic ballot. Chris Benham Juho wrote: On Nov 3, 2006, at 19:50 , Chris Benham wrote: Juho wrote: On Nov 2, 2006, at 1:29 , Kevin Venzke wrote: Juho, --- Juho [EMAIL PROTECTED] a écrit : Example 1. Large party voters consider C better than the other large party candidate, but not much. 45: LCR 40: RCL 15: CL=R Ranked Preferences elects L. (first round: L=-10, C=-70, R=-20; second round: L=-10, R=-20) In my opinion, if C is able to convince *every voter* to acknowledge that he is better than the major party alternative, then C is surely not a bad result. There is no need to convince every voter. This example is simplified (for readability) but not extreme since there could well be a mixture of different kind of votes. (See e.g. example 4.) The utility of C could be really low to the voters even though it was ranked higher than the worst candidate (in Range terms e.g. R=99, C=1, L=0). One of the key points of Ranked Preferences is that also weak preferences can be expressed and they may have impact. CB: So in your example is electing C a bad result or not?! I'd say it would be a bad result. If we only knew the flat preferences then C would be a good choice (Condorcet winner). But when we know the preference strengths electing C doesn't look sensible. We may have different ways to estimate at which point C should not be elected. Range would give one style of measuring it. Ranked preferences gave another one which I think is quite natural. I'd prefer methods where voters can simply vote sincerely without considering when it is beneficial to truncate and when not. Yes, don't we all. You like methods that meet Later-no-Harm and Later-no-Help, so how then is your method supposed to be better than IRV? This is a topic that I was planning to write more about. Ranked Preferences actually can support also IRV style voting in addition to Condorcet style flat preferences and many kind of more complex styles. IRV style ballots would look like ABCDE. If all voters vote this way the behaviour of the method resembles IRV. Voters are thus not forced to vote in IRV style but they can do so if they so want, possibly for defensive reasons (later-no-harm etc). The tied at bottom rule has also a similar defensive impact. I have no clear proofs (due to complexity and insufficient background work) but I believe the Ranked Preferences method quite well balanced e.g. in the sense that voting IRV style is not the only or recommended or optimal way to vote but just one of the alternatives, for voters that really feel that way. I hope the readers of this list will point out any potential weaknesses. I hope the method is better than IRV for the same reasons I believe it is (in some/many aspects) better than Condorcet. It is more expressive and therefore takes voter preferences better into account. Maybe without introducing too many weaknesses that would spoil the idea. Condorcet voters need not leave non-approved candidates unlisted. I think Ranked Preferences provides some improvements. I'll try to explain. If A and B voters would all truncate we would end up in bullet voting and falling to a plurality style election. Not a good end result. 45: LC=R 40: RC=L 15: CL=R Since it gives the same winner as your suggested method, why not? It gives the same winner in this particular case but not in general. And of course I try to make the method more expressive than Condorcet, not less expressive :-). (Range easily becomes Approval in competitive situations. I don't want Condorcet (or Ranked Preferences) to become Plurality.) I think it is a problem of basic Condorcet methods that they easily elect the centrist candidate. No, that is their theoretical strength. I agree that ability to elect centrist candidates is one of their strengths. I just want to add that centrist Condorcet winners are not always
Re: [EM] Ranked Preferences, example calculations
, the language is technical. Remember, the sincere vote here was A99B98. CB: The ranking was sincere but as I explained, the ratings maybe not. This is more interesting: 36: A99B98C0 18: B99B98C0 46: C99A0=B0 This time the AB faction have a comfortable enough majority to win without insincere equal-ranking, and A (the Condorcet and IRV winner) wins. But Range (like Approval) is vulnerable to a form of Burial with a nasty defection incentive. 36: A99B98C0 18: B99A0=C0 (sincere is BAC) 46: C99A0=B0 The 18 B voters have defected from the AB coalition by insincerely changing from B99A98 to B99B0=C0, and Range rewards their dishonesty (and disloyalty) by electing B. Now, why would they do this? Only if they strongly prefer B to A. But this contradicts the initial conditions. CB: Range only allows voters to express one strong (by your definition) preference (between two candidates or two sets of equally-ranked candidates). In the initial conditions the B supporters strongest preference was BC. Of course their sincere BA preference doesn't have to be all that strong for them to want to make B win. . And yet we imagine that the B voters are going to lie about their preference, in cahoots with each other, in order to elect B? CB: Who (besides you) mentioned anything about them being in cahoots with each other? No coordination is needed. As long as the other factions vote the same way, individual members of the B faction can try the strategy without any risk of it back-firing (and it can work if only some of them do it.) The Majority Criterion properly applies (i.e., is desirable) to binary elections. It gets dicey when there are more than two choices. CB: Why on earth is that, in your book? Strength of preference is all-important when there are three candidates, but not two? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Ranked Preferences, example calculations
Abd ul-Rahman Lomax wrote: At 11:34 PM 10/27/2006, Chris Benham wrote: Abd ul-Rahman Lomax wrote: That is, healthy group decision process follows certain general principles. The Majority Criterion neglects an important part of this. That is because it is about *elections*, which of course isn't necessarily the beginning and end of "healthy group decision process". For some reason, Chris continues to insist upon the specious distinction between elections and general decision-making process. The term "election" covers any kind of choice being made; however usage focuses on the selection of one candidate out of a number, for single-winner, or of multiple candidates out of a larger number, for mutiple-winner. And we also assume, generally, for the purposes of this list, that elections are of candidates, and the candidates are people who will hold an office. But for a group to select candidates or to select a pizza involves, properly, the same considerations. Pizza is almost certain to be less important a choice, but the importance of the choice only should mean that greater care would be taken. Not that a different process is involved. CB: No.I see "group decision making process" as spread out along a continuum with "informal consensus" at one end and civil war or violent "mob rule" at the other. Abd sees elections as (in his view undesirably) substituting for consensus and wants to change them into mechanisms for reaching a formal consensus, whereas I think they should more properly be seen as tough competitions that substitute for civil war. A group of people ordering pizza are presumably a freely associating group of friends, so all are considerate of the other's strong preferences (and "needs") and no-one wants to oppress anyone or listen to anyone whingeing while they are trying to enjoy their pizza. (And of course if anyone is really unhappy they can presumably just leave the group and not starve.)So in that case of course the group would probably quickly come to an informal consensus, and if there *was* any formal "voting" then I suppose some variation of Range or Approval would do and may be best. But suppose in an experiment to please Abd, the pizza orderers aren't friends and maybe even dislike each other, they are very hungry and there won't be enough pizza to satisfy everyone's hunger and the people are locked in the room with nothing to eat but this pizza they are ordering. Then "informal consensus" will tend to break down and we will have a scenario more appropriate for a tough election. Voters might have incentive to vote for a variety others dislike in the hope they will then get a bigger share. The only substantial argument I see against Range is that the method is allegedly vulnerable to strategic voting. *But what we have now is what Range would look like if everyone votes strategically.* So Range would not make things worth, unless... unless honest people vote intermediate values, and dishonest people vote the extremes, and there are enough of these dishonest people that election results are warped as a result. However, I have argued that this can only happen when the honest people do not have a strong preference. When they have, and express, a strong preference, and they are in the majority, the dishonest people can try what they may, they can only nudge the results among candidates strongly preferred by the majority. A "strong preference" for *what* exactly?.. that a single candidate be elected, that a single candidate not be elected, that the winner come from a certain set, what? Essentially, some writers treat the vulnerability of Range to strategic voting as if it were a proven thing. They simply assume it. It has *not* been proven, far from it. And it seems to me that this is a false charge against Range. It would. It is obvious to anyone with a clue that it is. E That is, if the majority does not want to please the minority, it does not care if they are devastated by the outcome of the election, if their attitude is "they should get over it," then they can easily get what they want. Just vote it as a strong preference. The problem with Range is that if "the majority" are not self-aware and coordinated, they cannot "easily get what they want". On the contrary, the condition being described was that the majority had a strong preference. Under Range, all they need to do is vote that preference as a strong one. What coordination does this take? Again "strong preference" for what exactly? And how strong is "strong"? This has been stated so many times by Warren, but obviously it bears repeating. The best vote in Range is a sincere one. Sure, partisans may distort
[EM] EM: 10 Steps to Repair American Democracy for only $2.99 on Amazon.com, forwarded from Steven Hill
Dear friends, I thought you might be interested in knowing about an amazing bargain -- right now Amazon.com is offering my book 10 Steps to Repair American Democracy for only $2.99. Yes, you read that correctly, only $3! I thought it must be a mistake, but one person I know just bought 40 copies at that price. Plus the shipping will be free for any order over $25, so this is an incredible bargain. Just in time to do some early Christmas shopping, at three dollars apiece 10 Steps to Repair American Democracy will make a great stocking stuffer. Ten books for $30 (and with free shipping for orders over $25, it's the same price to buy nine books as to buy six). I don't know how long this terrific price will last, it may be only for a limited time, so get them while you can. Here's a link to 10 Steps on Amazon http://www.amazon.com/gp/product/0976062151 Steven Hill's 10 Steps to Repair American Democracy is as practical as it is insightful, offering innovative ways to fix our broken political system. Read it, roll up your sleeves, and get to work. --- Arianna Huffington We are fortunate to have Steven Hill's latest book, 10 Steps to Repair American Democracy. He identifies ten critical problems with our democracy and offers concrete solutions to each one. 10 Steps is a blueprint for a reinvigoration of our republic. -- from the foreword by Hendrik Hertzberg, The New Yorker If you don't mind, please forward this to your own email lists. My apologies if you receive it more than once. Yours, Steven Hill P.S. in case you are interested, my recent lecture to the Cambridge Forum about 10 Steps to Repair American Democracy can be viewed on the web at http://forum.wgbh.org/wgbh/forum.php?lecture_id=3221. election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Majority Criterion poor standard for elections
Simmons, Forest wrote: It seems to me that if there is a majority winner, then she should at least have a chance of winning. What if we chose by random ballot from among all of the candidates that have a majority beat path to the Range winner (with a final approval vote to ratify this choice)? Why not just automate that and with one trip to the polls elect the winner of the pairwise comparison between the Range winner and a randomly chosen candidate with a beatpath to the Range winner, to make a pretty terrible method (but still better than Range) with a strong random element? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Condorcet + IRV completion?
Andrew Myers wrote:
Here's an obvious idea that must have been considered before. How about
using the basic Condorcet method, but running IRV on the Schwartz set,
if any? Are there any known results on how well this
works/vulnerabilities/etc.?
Andrew,
Yes. Douglas Woodall has demonstrated that dropping the non-members of
the Schwartz/Smith set
from the ballots and then applying IRV causes the resulting method to
fail both mono-add-plump
and mono-append, two very weak (normally easy to meet) criteria that I
rate a essential.
He refers to IRV as AV (Alternative Vote) and the Smith set as CNTT
(Condorcet(Net) Top Tier):
abcd 10
bcda 6
c 2
dcab 5
All the candidates are in the top tier, and the AV winner is a. But
if you add two extra ballots that plump for a, or append a to the two
c ballots, then the CNTT becomes {a,b,c}, and if you delete d from all
the ballots before applying AV then c wins.
But instead we don't need to even mention the Schwartz or any other set
in the algorithm:
Before the first and each subsequent IRV elimination, check to see if
the there is a single candidate X
with no (among remaining candidates) pairwise losses. As soon as an X
appears, elect X.
That *does* meet mono-append and mono-add-plump, with no disadvantage
compared to the other
method. Like IRV, it still fails mono-raise.
In common with IRV and Schulze it meets the Plurality criterion and
Clone Independence. In common
with other IRV methods, we lose IRV's Later-no-Harm and Mono-add-Top.
I like it, with above-bottom equal preferences not allowed so as to make
Pushover (turkey raising)
strategy more difficult.
It has the property that when there are three candidates XYZ, and X
wins with more than a third of the
first preferences, then changing some ballots from YXZ to YZX
can't change the winner to Y.
The other property that it has in common with IRV but not Schulze etc.
is that in the zero-information case
regardless of how the voter rates the candidates the voter has no
strategy that is better than sincere ranking.
Some dislike the fact that it fails Minimal Defense.
49: A
24: B
27: CB
Here it elects A.
46: AB
44: BC (maybe was BA or B)
10: C
Here I like the fact that it elects A. Meeting both MD and the
anti-burial property (Dominant Mutual Third Burial Resistance?)
would force the method to elect C.
Chris Benham
election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] DH3 pathology, margins, and winning votes
Warren,
Re: [EM] DH3 pathology, margins, and
winning votes
--- In [EMAIL PROTECTED],
Chris Benham [EMAIL PROTECTED] wrote:
Warren,
I have two main points in reply to your "DH3 pathology"
anti-Condorcet
argument.
DH3 scenario with strategic votes by the A- and B-voters.
#voters
Their Vote
37 CA,BD
32 ADB,C
31 BDA,C
Then the pairwise tallies are going to be:
Definitely A,B D C
Probably C A,B
In which case we (probably) have a Condorcet cycle scenario.
(It is
actually two 3-cycles which share the common DC arc.) The
weakest
defeats in these cycles are CA,B which means, under both
every
Condorcet rule I know of (since I think they all are
equivalent in the
3-cycle case) and Borda, that one of {A,B} is going to be the
winner.
I verified that A wins in the 50-50 mixture case under
Tideman ranked
pairs RankedPairs.html, Schulze beatpaths
SchulzeComplic.html, and
basic Condorcet by using Eric Gorr's Condorcet calculator
http://www.ericgorr.net/condorcet/
using this input
37:CABD
37:CBAD
32:ADBC
32:ADCB
31:BDAC
31:BDCA
The first is that those "defeat-dropper" style algorithms (like
Beatpath, Ranked Pairs, River,MinMax) that as you say are all
equivalent
in the 3-cycle case
are not my favourites. I prefer both DMC ('Definite Majority
Choice',
which allows voters to enter approval cutoffs) and Schwartz,IRV
(which
elects the
member of Schwartz set highest ordered by IRV on the original
ballots).
--Can you go thru how those two new methods would work?
CB: Certainly.
Schwartz,IRV:
"Identify the members of the Schwartz set, but drop no candidates from
the ballots.
Commence a normal IRV count. When all but one Schwartz set member x has
been
eliminated, elect x".
For this method I favour allowing truncation, but not above bottom
equal-ranking.
It is much better than Schwartz//IRV, which drops non-Schwartz set
members from
the ballots before applying IRV. Of course Smith verus Schwartz isn't
a big deal.
Definite Majority Choice.
"Voters submit ranked ballots with approval cutoffs. Truncation and
equal-ranking allowed.
Ballots with no approval cutoff specified are interpreted as approving
all candidates ranked
above bottom or equal-bottom.
Eliminate all candidates that are pairwise beaten by a more approved
candidate.
Among the remaining candidates, one (x) will pairwise beat all the
others.
Elect x."
http://wiki.electorama.com/wiki/DMC
Several other algorithms are equivalent. Also quite good in my opinion
is the simple version with
no approval cutoffs which just interprets all ranked (above
equal-bottom) candidates as approved .
My current favourite method that uses high-intensity range ballots is
this "automated version":
"Inferring ranking from ratings, eliminate all non-members of the
Schwartz set.
Then interpret the ballots as approving those candidates that they rate
(among those remaining)
above average (and half-approving those they rate exactly average).
Based on these thus derived approvals, and again inferring ranking from
ratings, apply DMC."
My second point is that in your scenario the A and B supporters
seem
mainly concerned to elect their favourites, so in that case why
wouldn't
they simply be guided in their strategy by their favourite
candidates? Seeing how
they stand in the polls, it would be in the interests of both A
and B to
make a preference-swap deal at the expense of C. That way they
each increase
their chances of being elected form below 33% to about 50% without
anyone
having to flirt with the car-crash.
--That sounds like naive bunk.
The problem with that is, how the hell do voters "make a deal" with
each other? This whole "deal" idea is a myth. It is unenforcable and
votes are secret ballot and nobody can make a deal with a gazillion
voters anyhow even if it were enforceable and verifiable.
CB: "Naive bunk"? It is regular practice in Australian elections for
seats in Parliament.
Admittedly this is helped a lot in most jurisdictions by truncation not
being allowed.
The candidates are normally obliged to register "tickets" with the
electoral commission
in advance of the election, partly so attempts to manipulate the result
by distributing bogus
"how-to-vote" cards can be detected and stamped on.
Unless there is automatic and/or long standing cooperation based on
ideological affinity
the parties/candidates negotiate preference deals with each other.
Party volunteers on
election day hand out how-to-vote cards to voters on their way in to
vote. Most voters
take at least one and follow one of them.
In your example, based on the sincere preferences, the candidates seem
to be about equidistant
from each other on the "political spectrum". With a clear front-runner
(C) and the other two
(A and B) too close to call, the A and B candidates both gain a lot
from swapping preferences.
If the vo
Re: [EM] DH3 pathology, margins, and winning votes
Warren, BTR-IRV can entirely eliminate the Smith set and elect some nonmember. How can it possibly do that? Chris Benham Warren Smith wrote: Sorry, my last email was in error: BTR-IRV can entirely eliminate the Smith set and elect some nonmember. wds election-methods mailing list - see http://electorama.com/em for list info election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] DH3 pathology, margins, and winning votes
Warren, DH3 scenario with strategic votes by the A- and B-voters. #voters Their Vote 37 CA,BD 32 AD=B=C 31 BD=A=C Aren't the A and B voters here (in effect) just truncating? Chris Benham Warren Smith wrote: Sorry, for some reason, the hyperlink in my previous post was omitted. Let me try again: http://rangevoting.org/WinningVotes.html election-methods mailing list - see http://electorama.com/em for list info
[EM] Report of the Irish Commission on Electronic Voting
I've been advised that this is important and recently released. http://www.cev.ie/htm/report/download_second.htm Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] Forwarded from Steven Hill, his WA Post oped: Will Your Vote Count in 2006?
Will Your Vote Count in 2006? By Steven Hill Special to washingtonpost.com's Think Tank Town Tuesday, August 1, 2006; 11:56 AM http://www.washingtonpost.com/wp-dyn/content/article/2006/08/01/AR2006080100561.html Watching Mexico live through a controversial presidential election was like holding up a mirror to our own election difficulties in recent years. As we round the corner and head toward the upcoming November elections -- with control of the Congress up for grabs -- what can Americans expect? Will our votes count? There is both cause for worry, as well as signs that effective voting reform advocacy is paying off. The root cause of our troubled elections is that, unbelievably, the U.S. provides less security, testing, and oversight of our nation's voting equipment and election administration than it does to slot machines and the gaming industry. Our elections are administered by a hodgepodge of over 3000 counties scattered across the country with minimal national standards or uniformity. Widely differing practices on the testing and certification of voting equipment, the handling of provisional and absentee ballots, protocols for recounts, and training of election officials and poll workers makes for a bewildering terrain. About Think Tank Town Washingtonpost.com edits and publishescolumnssubmitted by10 prominent think tanks on a rotating basis every other weekday. Each think tankis free to choose its authors and the topics it believes are most important and timely. Here are the participating organizations: American Enterprise Institute Brookings Institution Cato Institute Center for American Progress Center for Strategic and International Studies Council on Foreign Relations Heritage Foundation New America Foundation RAND Corporation Urban Insitute The three federal laboratories testing voting equipment and software operate with little government oversight. They are called "independent testing authorities," even though two of them have donated tens of thousands of dollars to GOP candidates and the Republican National Committee. The shoddy testing and certification procedures are greased by a revolving door between government regulators and the industry. Former secretaries of state from California, Florida and Georgia, once their state's chief regulator, became paid lobbyists for the corporate vendors after stepping down from public office, as did a former governor of New Hampshire. Several secretaries of state in 2004 served as co-chairs of the George W. Bush re-election campaign for their state; one of these oversaw the election in which he ran -- successfully -- for governor. Conflicts of interest have crept like a weed into nearly every crevice of election administration. Making matters worse, the powers-that-be appear uncertain about what a secure election administration system actually looks like. This was painfully obvious at the Voting Systems Testing Summit in November 2005, which marked the first time that top federal regulators, vendors, testing laboratories, election administrators, computer scientists and fair elections advocates came together in one place. No one could articulate a comprehensive inventory of the many problems in securing the vote, much less the solutions. Instead, there was a lot of finger-pointing and excuses. Clearly, the biggest threat to the integrity of our elections is not the shortcomings of any particular type of computerized voting equipment but the fact that -- like the failed rescue effort following Hurricane Katrina -- no one seems to be steering the ship. There is no central brain or team that has a handle on all aspects of the process, developing best practices or a roadmap that states and counties can follow. Tragically, while Congress has appropriated $3 billion for buying new voting equipment, the money is arriving before there are necessary standards in place to ensure the money is not wasted. Yet these legitimate concerns also must be kept in perspective, lest we spiral into a paralyzing paranoia. There are a number of positives. Election security activists are more mobilized than ever and they are having an impact. They have raised the profile of these issues to the point of national urgency. Their efforts, once considered the actions of fanatical gadflies, are being increasingly cited by respected election bureaucrats. Former President Jimmy Carter and Secretary of State James A. Baker III were co-chairs of a 2005 bipartisan commission which warned that "software can be modified maliciously before being installed into individual voting machines. There is no reason to trust insiders in the election industry any more than in other industries." Reform advocates' increased credibility has
Re: [EM] voting reform effort in DENVER - PLEASE HELP
-winner alternatives to IRV, your list should include both versions of Definite Majority Choice(DMC): the one that interprets all ranked candidates as approved (of course allowing truncation), and the one that allows voters to enter an approval cutoff so that they can rank unapproved candidates. This has two simple definitions: (1) Elect the CW if there is one. If not, eliminate (drop from the ballots) the least-approved candidate. Repeat until there is a winner. (2) Eliminate all candidates that are pairwise-beaten by a more-approved candidate. One of the remaining candidates x will pairwise beat all the other remaining candidates. Elect x. This method meets Condorcet, Clone Independence and Mono-raise. Number 4 on your list is all wrong. As I understand it, BTR-IRV stand for Bottom Two Runoff-IRV, which at each stage eliminates the pairwise-loser of the two remaining candidates with the fewest top-preferences. It's just an attempt to smuggle a not very good Condorcet method past IRV supporters. Neither it nor the method you define is equivalent to Condorcet with Plurality completion. The method you define is Coombs or one of the two versions of Coombs (the worse one). It is far worse than IRV. The version you give fails Majority Favourite. It is possible that a candidate with more than half the first preference votes will be eliminated. (The other version has a majority stopping rule). Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Correlated Instant Borda Runoff, without Borda
Dan, Dan Bishop wrote: *** EXAMPLE: CLONE-TRANSFER APPROXIMATION OF IRV *** Consider the election method: count the first-choice votes of each candidate while no candidate has a majority of the vote: eliminate the last-place candidate transfer that candidate's votes to their most-correlated candidate elect the candidate with a majority of a vote I can't see any justification for this (versus proper IRV) at all. If we eliminate candidates and transfer votes, then I can't see how we can justify not transferring them exactly where they want to go (or any point in not doing that). As I understand it, Kuhlman's Correlated Instant Borda Runoff was conceived of as way of decloning Borda. IRV is already Clone Independent, and so doesn't need decloning! Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] [ER] FBC-complying Margins-like method (?)
Kevin, Warren, other FBC freaks, I've recently had an idea for a FBC-complying Margins method. Voters rank the candidates, equal-ranking and truncation allowed. (1) Make pairwise comparisons. Treating pairwise defeats by margins that are smaller than or equal to the number of ballots on which both candidates are ranked equal-top as pairwise equalities, eliminate candidates that are not in the smallest non-empty set of candidates that are pairwise undefeated by any outside-the-set candidates. (2)If more than one candidate remains, drop eliminated candidates from the ballots and then delete ballots that make no ranking distinction between remaining candidates, and repeat step 1. (3) Repeat steps 1 and 2 as many times as possible. (If at any stage only one candidate remains then that candidate is the winner.) (4) If after step 3 more than one candidate remains, then with ballots that rank both the candidates in a pairwise comparison equal-top used to modify the defeat margins by counting as whole single votes for the pairwise loser (so that some margins can be negative, but not so that any pairwise defeats can be reversed); change the pairwise defeat by a smallest margin to an equality; and as in step 1 again eliminate candidates that are not in the smallest non-empty set of candidates that are pairwise undefeated by any outside-the-set candidates. (5) If more than one candidate remains, then again drop eliminated candidates from the ballots and then delete ballots that make no ranking distinction between remaining candidates. (6) Keep repeating steps 4 and 5 until only one candidate remains. In common with MDD,ER-Bucklin(whole) I think it meets Majority for Solid Coalitions and Condorcet(Gross). But unlike that method, it meets Independence from Irrelevant Ballots. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] [ER] FBC-complying Margins-like method (?)
Kevin, Yes I am sure you are right, thanks. Probably then I'll stick with MDD,ER-Bucklin(whole) as my favourite FBC method. Chris Benham Kevin Venzke wrote: Chris, --- Chris Benham [EMAIL PROTECTED] a écrit : Kevin, Warren, other FBC freaks, I've recently had an idea for a FBC-complying Margins method. Voters rank the candidates, equal-ranking and truncation allowed. (1) Make pairwise comparisons. Treating pairwise defeats by margins that are smaller than or equal to the number of ballots on which both candidates are ranked equal-top as pairwise equalities, eliminate candidates that are not in the smallest non-empty set of candidates that are pairwise undefeated by any outside-the-set candidates. (2)If more than one candidate remains, drop eliminated candidates from the ballots and then delete ballots that make no ranking distinction between remaining candidates, and repeat step 1. There are two reasons why I don't believe this can work. 1. You're using a beatpath concept. Although you're replacing certain wins with pairwise ties, it could be that a pairwise tie between X and Y is what causes them to be excluded from the top tier. Replacing wins with ties only helps to satisfy FBC when it's clear that a tie between X and Y is at least as good for them as one of them beating the other. 2. You're eliminating candidates and recalculating. I think all you can afford to do is disqualify candidates without recalculating anything. Elimination makes it difficult to foresee what a specific vote is capable of doing across multiple rounds. It's much the same issue as Raynaud or Nanson failing monotonicity. Kevin Venzke election-methods mailing list - see http://electorama.com/em for list info
[EM] Bucklin PR ?
Kevin, I see from your response to the Electowiki Method support poll that you nearly support the ER-Bucklin(whole) single-winner method, and that for Legislative election methods you like possibly a proportional approval scheme. What do you think of this PR version of ER-Bucklin(whole) ? Voters rank candidates, truncatation and equal-ranking ok. The winning threshold to elect the first winner is a Droop quota (number of valid ballots/number of seats +1). (1) Commence the ER-Bucklin(whole) process until the candidate with the highest score has a winning threshold. Declare that single candidate elected. (2) Reduce the weight of all the ballots that contributed to the winner's tally by an equal amount which sums to a Droop quota. (3) Based on these reweighted ballots, the reduced number of unfilled seats, and not counting as valid any now exhausted ballots, reset the Droop quota. (4) Repeat the above three steps until all the seats are filled. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] oped in Mercury News on Citizens' Assemblies (forwarded from Steven Hill)
From: Steven Hill, New America Foundation Dear friends, I have an oped in yesterday's San Jose Mercury News about Citizens' Assemblies as a vehicle for political reform. I thought you would find it interesting. Please forward to your lists and others interested. Thanks, Steven Hill In Canada, regular folks are put to work on reforms By Steven Hill San Jose Mercury News Wed, Nov. 16, 2005 http://www.mercurynews.com/mld/mercurynews/news/opinion/13180228.htm Despite voters rejecting Gov. Arnold Schwarzenegger's attempts to end-run the Legislature, that does not mean voters don't want change. California's political leaders must try to pick up the pieces of what is left of state politics. The challenges are daunting, particularly because both the governor and Legislature have lost so much credibility. The question is: How do we move forward? One of the solutions may lie across the border in Canada. It's called a Citizens' Assembly, and it was on display last year in the province of British Columbia. The government there turned over to the people the task of basic political reform, and by doing so took the partisanship out of the process, something California badly needs. Here's how it worked: The government randomly selected 160 average citizens to participate in the Citizens' Assembly, like selecting a jury pool. The Assembly had 80 women and 80 men from all of the province's 79 electoral districts. It was an independent, non-partisan body charged with a particular focus: to examine British Columbia's electoral system, and how their winner-take-all system was performing in determining who got elected to the Legislature. This effort was unique. Often such task forces are dominated by the usual political insiders or good-government activists. Nowhere in the world had randomly selected citizens with no history of interest in electoral reform been so empowered to shape major proposals. Yet the work of the Assembly was unanimously endorsed by the political parties in the Legislature and community leaders. The Assembly's tenure was divided into three phases: Learning about reform, January-March 2004; public hearings, May-June; and deliberations, September-November. They met on weekends, their expenses and a small per diem paid for by the government. They were visited by top experts from all political perspectives who gave them the benefit of their knowledge and analysis. The Assembly delivered a final report in December 2004. It voted 146-7 to toss out its longtime winner-take-all, single-seat district electoral system and replace it with a proportional representation system. ``This really is power to the people,'' enthused Jack Blaney, the chair of the Citizens' Assembly. The Assembly's proposal was submitted by the legislature directly to the voters in a referendum last May. Because the Citizens' Assembly was composed of average citizens, their recommendation had tremendous legitimacy with the public. A robust 58 percent of voters supported the measure. The Citizens' Assembly in British Columbia focused on the electoral system, but the focus just as well could have been on other aspects of the political system. In California, a Citizens Assembly could focus on redistricting reform or campaign finance reform; or reforming our broken primary system and the electoral system. The Citizens' Assembly solves a real dilemma: How do we enact meaningful political reform, which California so badly needs, when both the governor and the Legislature have conflicts of interest that induce them to manipulate the rules in their favor? Citizens' Assemblies could be important vehicles for modernizing our political system because trust is placed in average citizens who have more credibility than the political class. If you truly believe in democracy, that's where trust belongs. In the mid-1990s, a California Constitutional Revision Commission deliberated on some of these fundamental issues, but it was too timid and politically weak to enact change. The Citizens' Assembly points the direction that Schwarzenegger and Democrats in the Legislature should lead. The governor opened the debate with redistricting reform, but now is the time to inject fairness and non-partisanship into state politics. What better way than by establishing a Citizens' Assembly that empowers average citizens to decide what political reform is best for California? STEVEN HILL is an Irvine senior fellow with the New America Foundation and author of ``Fixing Elections: The Failure of America's Winner Take All Politics'' (www.fixingelections.com). To find out more about British Columbia's Citizens' Assembly, visit www.citizensassembly.bc.ca election-methods mailing list - see http://electorama.com/em for list info
[EM] Two round system (improved Approval version)
Juho, I see from the Method support poll that you are close to supporting a Two round system. I regard the normal version of this, where both rounds are by Plurality and the top two from the first round run off in the second, as pretty awful. The only criterion compliance advantage it has over FPP is Condorcet Loser, and generally the only thing good about it is that its equivalent to IRV when there are three (or fewer) candidates. One attempted improvement I've seen suggested is to use Approval in the first round, and then have the two most approved candidates run off in the second. Unfortunately that would be a strategy farce because rich parties with some hope of coming first in the Approval round will have an incentive to gain an unfair advantage by each running two candidates, plus many voters will have incentive to engage in easy Pushover strategizing by approving both their sincere favourite/s and the candidate that they think their favourite can most easily beat in the second round. With too much of that, it is possible that both of the finalists will be turkeys. I've recently had an idea on how to fix this without, say, having votes cast in the first round also count in the second. The first round uses approval ballots. If there is a second round, it is between two candidates. The first candidate to qualify for the second round is the Approval winner (A) Of those candidates B whose approval scores would exceed A's if ballots that approve both or neither of A and B were altered so that they only approve of B, select as the second qualifier the candidate that is most approved on ballots that don't approve A. If there are none such candidates B, then there is no second round and A is elected. Of course it is possible to automate this into a single-round method that uses ranked ballots with an approval cutoff, but that would fail the Plurality criterion, the Irrelevant Ballots criterion and probably some (maybe more serious) others. (Here by round I mean trip to the polling stations, with the results of any previous round in the same election known to the voters.) 49: A 24: B 27: CB (CB, both approved) Here the two finalists are B and C. In the single-round version, C would win, failing the Plurality criterion. A simpler version which is more often decisive in the first round but has a greater later-harm problem would only consider the candidate that is most approved on ballots that don't approve the approval winner (i.e. has the greatest approval opposition to the approval winner) for the position of second qualifier. In the above example that would be A, who would be rejected and so B would be elected in the first round. But then the C supporters could have got C into the second round (with A) by only approving C. One possible problem with this idea of mine is that it may not be widely seen/understood as legitimate that there may be a candidate or candidates that don't make it into the second round but have a higher approval score than the second qualifier. The only way around that is to relax the insistence that only two candidates go into the second round, and say that all candidates with approval scores higher than the second qualifier's also qualify for the second round. (If there are more than two candidates in the second round, then if we want to keep it a binary-input system, Approval should be used instead of FPP.) In the above example that would presumably mean that again B would be elected in the first round, unless perhaps A volunteers to drop out, because otherwise all three candidates qualify. I bring this up for jurisdictions which for some reason want to keep having two election rounds, each with the voters giving simple binary inputs. Do you think the French will like it? Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] simple question (I think)
Rob, rob brown wrote: For instance, say there is no Condorcet winner. Candidates A, B and C all have 8 pairwise wins. D has 7. Could D still be chosen as the winner by any reasonable method? Yes. The method that just counts the number of pairwise wins is called Copeland. It hopelessly fails Clone Independence (Clone-Loser) and Rich Party. Imagine that that there are three candidates, each with the same number of pairwise wins, and the Condorcet method elects X. Say that the top cycle is XZYX Now say we add a clone of Y, that every voter ranks directly below Y. Now Y and Z will each have an extra pairwise win, one more than X and so now (by the Copeland criterion) X must lose to Z or Y. Adding a clone of a losing candidate (not to say adding a Pareto-dominated candidate) has changed the winner. Parties and factions that run more candidates will have an absurd and unfair advantage. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] STV-PR is not reweighted IRV and not House-Monotonic (was corrections to older posts re IRV public election data)
Warren Smith wrote: Arguably STV multiwinner elections are still of interest for single-winner purposes since the FIRST winner is a single-winner IRV winner. This seems to imply that multi-winner STV meets House-Monotonicity: No candidate should be harmed by an increase in the number of seats to be filled, with no change in the profile. It doesn't and shouldn't. Multi-winner STV is not re-weighted IRV. In this Dec.1914 article, Woodall discusses this. http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM http://groups.yahoo.com/group/election-methods-list/files/wood1994.pdf He mentions this example: 2 seats. 36: AD 34: BD 30: CD Condorcet supporters would all agree that the best candidate to fill a single seat is D, but to fill two seats the Droop proportionality criterion (DPC) says that we must elect A and B. Quoting from that article: The most important single property of STV is what I call the /Droop proportionality criterion/ or /DPC/. Recall that if /v/ votes are cast in an election to fill /s/ seats, then the quantity /v//(/s/ + 1) is called the /Droop quota/. * *DPC.* If, for some whole numbers /k/ and /m/ satisfying 0 /k/ = /m/, more than /k/ Droop quotas of voters put the same /m/ candidates (not necessarily in the same order) as the top /m/ candidates in their preference listings, then at least /k/ of those /m/ candidates should be elected. (In the event of a tie, this should be interpreted as saying that every outcome that is chosen with non-zero probability should include at least /k/ of these /m/ candidates.) In statements of properties, the word should indicates that the property says that something should happen, not necessarily that I personally agree. However, in this case I certainly do: DPC seems to me to be a /sine qua non/ for a fair election rule. I suggest that any system that satisfies DPC deserves to be called a /quota-preferential/ system and to be regarded as a system of proportional representation (within each constituency)-an STV-lookalike. Conversely, I assume that no member of the Electoral Reform Society will be satisfied with anything that does not satisfy DPC. The property to which DPC reduces in a single-seat election should hold (as a consequence of DPC) even in a multi-seat election, and it deserves a special name. * *Majority.* If more than half the voters put the same set of candidates (not necessarily in the same order) at the top of their preference listings, then at least one of those candidates should be elected. It is possible for multi-winner STV to fail to elect the IRV winner. Adapting an old example from Adam Tarr: 3 seats, 100 ballots.. 08: FRRLRMRML 02: RFRLRMRML 04: RLRFRMRML 07: LRMRRML 15: MRLRMLR 16: MLMRLRL 15: MLLMRFLLR 13: LMLFL 11: LFLML 09: FLLMLMR The IRV winner is Lucky Right(LR), but 3- winner STV elects first ML, then Left, then MR. The Droop quota is 25. Moderate Left(MR) is the only candidate that starts with a quota so is first elected. Then 15/31 of Moderate Left's surplus 6 votes go to Left, which raises Left from 24 to 26.903 so now Left has a quota and so is second elected. The other 16/31 of ML's surplus 6 votes go to MR, raising MR from 15 to 18.09677votes. Then MR also gets all of L's surplus of 1.903 votes (all originally from ML) to raise L's score to 20 votes. The tallies for the remaining unelected candidates are FR8, R6, LR7, MR20, FL9. None have a quota so we eliminate R, which gives FR10, LR11, MR20, FL9. None have a quota so we eliminate FL, which gives FR10, LR11, MR29. MR now has a quota so is the last candidate elected. In the IRV election the elimination order is R, FL, FR, MR, ML, L. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] STV-PR is not reweighted IRV and not House-Monotonic (was corrections to older posts re IRV public election data)
Warren Smith wrote: Arguably STV multiwinner elections are still of interest for single-winner purposes since the FIRST winner is a single-winner IRV winner. This seems to imply that multi-winner STV meets "House-Monotonicity": "No candidate should be harmed by an increase in the number of seats to be filled, with no change in the profile". It doesn't and shouldn't. Multi-winner STV is not "re-weighted IRV". In this Dec.1914 article, Woodall discusses this. http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM http://groups.yahoo.com/group/election-methods-list/files/wood1994.pdf He mentions this example: 2 seats. 36: AD 34: BD 30: CD Condorcet supporters would all agree that the best candidate to fill a single seat is D, but to fill two seats the "Droop proportionality criterion" (DPC) says that we must elect A and B. Quoting from that article: The most important single property of STV is what I call the Droop proportionality criterion or DPC. Recall that if v votes are cast in an election to fill s seats, then the quantity v/(s + 1) is called the Droop quota. DPC. If, for some whole numbers k and m satisfying 0 k = m, more than k Droop quotas of voters put the same m candidates (not necessarily in the same order) as the top m candidates in their preference listings, then at least k of those m candidates should be elected. (In the event of a tie, this should be interpreted as saying that every outcome that is chosen with non-zero probability should include at least k of these m candidates.) In statements of properties, the word "should" indicates that the property says that something should happen, not necessarily that I personally agree. However, in this case I certainly do: DPC seems to me to be a sine qua non for a fair election rule. I suggest that any system that satisfies DPC deserves to be called a quota-preferential system and to be regarded as a system of proportional representation (within each constituency)-an STV-lookalike. Conversely, I assume that no member of the Electoral Reform Society will be satisfied with anything that does not satisfy DPC. The property to which DPC reduces in a single-seat election should hold (as a consequence of DPC) even in a multi-seat election, and it deserves a special name. Majority. If more than half the voters put the same set of candidates (not necessarily in the same order) at the top of their preference listings, then at least one of those candidates should be elected. It is possible for multi-winner STV to fail to elect the IRV winner. Adapting an old example from Adam Tarr: 3 seats, 100 ballots.. 08: FRRLRMRML 02: RFRLRMRML 04: RLRFRMRML 07: LRMRRML 15: MRLRMLR 16: MLMRLRL 15: MLLMRFLLR 13: LMLFL 11: LFLML 09: FLLMLMR The IRV winner is "Lucky Right"(LR), but 3- winner STV elects first ML, then Left, then MR. The Droop quota is 25. Moderate Left(ML) is the only candidate that starts with a quota so is first elected. Then 15/31 of Moderate Left's surplus 6 votes go to Left, which raises Left from 24 to 26.903 so now Left has a quota and so is second elected. The other 16/31 of ML's surplus 6 votes go to MR, raising MR from 15 to 18.09677votes. Then MR also gets all of L's surplus of 1.903 votes (all originally from ML) to raise L's score to 20 votes. The tallies for the remaining unelected candidates are FR8, R6, LR7, MR20, FL9. None have a quota so we eliminate R, which gives FR10, LR11, MR20, FL9. None have a quota so we eliminate FL, which gives FR10, LR11, MR29. MR now has a quota so is the last candidate elected. In the IRV election the elimination order is R, FL, FR, MR, ML, L. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] STV-PR is not reweighted IRV and not House-Monotonic (was corrections to older posts re IRV public election data)
Sorry about the multiple posting. In my explanation below of the STV procedure for my example, I wrote: Then MR also gets all of L's surplus of 1.903 votes (all originally from ML) to raise L's score to 20 votes. Of course it is MR whose score is raised to 20 votes. (corrected version below). Chris Benham Chris Benham wrote: Warren Smith wrote: Arguably STV multiwinner elections are still of interest for single-winner purposes since the FIRST winner is a single-winner IRV winner. This seems to imply that multi-winner STV meets "House-Monotonicity": "No candidate should be harmed by an increase in the number of seats to be filled, with no change in the profile". It doesn't and shouldn't. Multi-winner STV is not "re-weighted IRV". In this Dec.1914 article, Woodall discusses this. http://www.mcdougall.org.uk/VM/ISSUE3/P5.HTM http://groups.yahoo.com/group/election-methods-list/files/wood1994.pdf He mentions this example: 2 seats. 36: AD 34: BD 30: CD Condorcet supporters would all agree that the best candidate to fill a single seat is D, but to fill two seats the "Droop proportionality criterion" (DPC) says that we must elect A and B. Quoting from that article: The most important single property of STV is what I call the Droop proportionality criterion or DPC. Recall that if v votes are cast in an election to fill s seats, then the quantity v/(s + 1) is called the Droop quota. DPC. If, for some whole numbers k and m satisfying 0 k = m, more than k Droop quotas of voters put the same m candidates (not necessarily in the same order) as the top m candidates in their preference listings, then at least k of those m candidates should be elected. (In the event of a tie, this should be interpreted as saying that every outcome that is chosen with non-zero probability should include at least k of these m candidates.) In statements of properties, the word "should" indicates that the property says that something should happen, not necessarily that I personally agree. However, in this case I certainly do: DPC seems to me to be a sine qua non for a fair election rule. I suggest that any system that satisfies DPC deserves to be called a quota-preferential system and to be regarded as a system of proportional representation (within each constituency)-an STV-lookalike. Conversely, I assume that no member of the Electoral Reform Society will be satisfied with anything that does not satisfy DPC. The property to which DPC reduces in a single-seat election should hold (as a consequence of DPC) even in a multi-seat election, and it deserves a special name. Majority. If more than half the voters put the same set of candidates (not necessarily in the same order) at the top of their preference listings, then at least one of those candidates should be elected. It is possible for multi-winner STV to fail to elect the IRV winner. Adapting an old example from Adam Tarr: 3 seats, 100 ballots.. 08: FRRLRMRML 02: RFRLRMRML 04: RLRFRMRML 07: LRMRRML 15: MRLRMLR 16: MLMRLRL 15: MLLMRFLLR 13: LMLFL 11: LFLML 09: FLLMLMR The IRV winner is "Lucky Right"(LR), but 3- winner STV elects first ML, then Left, then MR. The Droop quota is 25. Moderate Left(ML) is the only candidate that starts with a quota so is first elected. Then 15/31 of Moderate Left's surplus 6 votes go to Left, which raises Left from 24 to 26.903 so now Left has a quota and so is second elected. The other 16/31 of ML's surplus 6 votes go to MR, raising MR from 15 to 18.09677votes. Then MR also gets all of L's surplus of 1.903 votes (all originally from ML) to raise MR's score to 20 votes. The tallies for the remaining unelected candidates are FR8, R6, LR7, MR20, FL9. None have a quota so we eliminate R, which gives FR10, LR11, MR20, FL9. None have a quota so we eliminate FL, which gives FR10, LR11, MR29. MR now has a quota so is the last candidate elected. In the IRV election the elimination order is R, FL, FR, MR, ML, L. 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
Re: [EM] Beatpath and SSD aren't manipulable. Manipulable is barking up the wrong tree.
MIKE OSSIPOFF wrote: Warren-- You wrote: I would expect it [beatpath] is extremely manipulable. I reply: Critics of pairwise-count methods speak of how they're vulnerable to two offensive strategies: Truncation and offensive order-reversal. And, for all Condorcet methods other than Condorcet(wv), they're right. All Condorcet methods that don't use winning-votes are a strategic mess, just as you suspect. But wv is different. You're ignoring the distinction between different kinds of Condorcet. 46: AB 44: BC (sincere is B or BA) 10: C The defeat-dropper style Condorcet(wv) method you refer to here elects B. This looks a lot like vulnerability to offensive order-reversal (aka Burial strategy) to me. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] MDD,ER-Bucklin (whole)
Participants, I've recently had the idea that ER-Bucklin (whole) could be improved by combining it with the "Majority-Defeat Disqualification" (MDD) component from MDD//Approval (MDDA). So I suggest MDD,ER-Bucklin(whole) as my favourite method that meets FBC. "Voters rank the candidates, truncation and equal-ranking allowed. If not all candidates are majority-strength pairwise beaten (i.e."dominated") by some other candidate, then "disqualify" (but not drop from the ballots) those that are. If only one candidate remains, that candidate wins. If more than one candidate remains, commence the ER-Bucklin(whole) process until (at least) one of the not-disqualified candidates has a vote tally greater than (or equal to) half the total number of valid ballots. At that point elect the not-disqualified candidate with the highest vote tally." [The "(or equal to)" bit isn't traditional, but I suspect as a fine point it is good.] To explain "the ER-Bucklin(whole) process": "In the first round each ballot contributes a whole vote each to the tallies of those candidates they rank top or equal-top. In the second round, ballots that have contributed to the tallies of less than two candidates each contribute a whole vote each to the tallies of candidates they rank second or equal-second. (Ballots that in the first round contributed to the tallies of more than one candidate do nothing in the second round) In the third round, if there is one, ballots that have contributed to the tallies of less than three candidates now contribute a whole vote each to the tallies of candidates they rank third or equal-third. And so on." Or as it is better explained at the Electowiki: If a ballot lists n candidates as tied in kth place, count that ballot as a whole point for all n candidates beginning in the kth round. Note: A candidate is ranked in kth place on a given ballot if there are k-1 candidates who are ranked strictly higher. For exampe, a ballot marked AB=C=DEF=G=H=IJ should be considered to rank A to in 1st place, B, C, and D in 2nd place, E in 5th place, F, G, H, and I in 6th place, and J in 10th place. Thus, the ballot would not count in favor of E until the 5th round, and it would not count in favor of J until the 10th round. This rule is perhaps unique in that it satisfies both the "favorite betrayal" criterion and the Majority criterion for solid coalitions. If the majority-disqualified candidates were dropped from the ballots, then Bucklin's compliance with Mono-raise would (I presume) be lost. (If I'm wrong about, then there probably isn't any reason not to just first drop them from the ballots, making the method the simpler and more "intuitive" MDD//ER-Bucklin(whole).) I think the only criterion compliance of plain ER-Bucklin(whole) that we lose is "Later-no-Help", which I don't expect anyone will miss. What we gain is "Smith-Condorcet (Gross)" (which means that the winner comes from the smallest non-empty set of candidates that all majority-strength pairwise beat any and all outside-the-set candidates) and the Strategy-Free Criterion (SFC) . Electowiki definition of SFC: If a Condorcet candidate exists, and if a majority prefers this candidate to another candidate, then the other candidate should not win if that majority votes sincerely and no other voter falsifies any preferences. In a ranked method, it is nearly equivalent to say: If more than half of the voters rank x above y, and there is no candidate z whom more than half of the voters rank above x, then y must not be elected. The method meets FBC/Sincere Favourite, Majority for solid coalitions/Mutual Majority, the Plurality criterion, Smith(Gross), SFC (and GSFC?). It fails Clone Independence (doubtless both Clone-Winner and Clone-Loser), Later-no-Harm, Independence from Irrelevant Ballots, No Zero-Information Strategy. Compared to plain ER-Bucklin(whole), this method would have a less severe Later-no-Harm problem. In ER-Bucklin(whole), if the voter has a big sincere approval cutoff, the s/he should equal-rank above it and truncate below it. In MDD,ER-Bucklin(whole), if the voter's sincere approval cutoff is above the most preferred member of the anticipated sincere Smith set then it is probably safe to truncate below that candidate. In my view the worst feature of this method is its bad clone problem. Also I dislike methods that fail Irrelevant Ballots (in the same spirit as the "Blank Ballots Criterion"). But combining FBC with Majority for solid coalitions and Smith(Gross) in my view makes it an ok package, better than MDDA. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] full ranks in MDDA (not)
Warren Smith wrote: A. I would prefer it if MDDA actually forbids approving everybody e.g. by saying if you rank them all, then the last is automatically disapproved. Then we are sure and do not have to depend on this assumption. I agree with this, and the same for all implicit approval methods. B. If last-not-approved-only behavior is very common then the result will be AntiPlurality voting to do the approvals. AntiPlurality voting is a very bad system in which with strategy a dark horse always wins. So this gives me bad vibes. Seem to me this might happen in a substantial subclass of elections - then things could still be bad, albeit in a different way. I agree with this, but MDDA is being promoted for public political elections with a lot winning-probability information and a lot of strategic voters (who are happy to truncate and Compromise-compress). Chris Benham election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Warren: MDDA vs RV, 10/16/05
Mike, You wrote: There's only one way to count RV or Approval ballots: Add them up. In the case of RV ballots, there is also Average Rating and Median Rating and also rankings can be inferred and used. And there are probably other ways. On the RV list, someone mentioned the idea of discarding outliers as in Olympic scoring. Chris Benham election-methods mailing list - see http://electorama.com/em for list info
[EM] which voting methods fail WMW?
Warren Smith (Wed.Oct.5): wds: Robla failed to mention that range voting *does* obey a weakened form of the majority-winner criterion (call it "WMW"). Specifically: "If a strict majority of the voters regard X as their unique favorite, then they, acting alone without regard to what the other voters do, can force his election." I don't know about you, but I personally regard WMW as a more-desirable critrion for a voting system to obey, than Anderson 1994's MW criterion. Chris Benham: Are there any methods actually *fail* this criterion? Borda perhaps? --response by wds: yes, Borda fails it. So does the somewhat Borda-like method used on the Island of Nauru. So does Coombs' IRV-like voting method. Also Ken Arrow's favorite voting method (or so I heard) the Arrow-Raynaud method, fails this test. Range voting, however, passes this test. wds Warren, I've seen Coombs defined with and without a majority-stopping rule. (To me not having it seems worse and odd). I assume you are referring to the version without: http://cec.wustl.edu/~rhl1/rbvote/desc.html The candidate with the largest last-rank total is eliminated. The last-rank totals are recalculated and the step repeated until only one remains. The other version seems more common: http://wiki.electorama.com/wiki/Coombs%27_method Each voter rank-orders all of the candidates on their ballot. If at any time one candidate is ranked first (among non-eliminated candidates) by an absolute majority of the voters, then this is the winner. As long as this is not the case, the candidate which is ranked last (again among non-eliminated candidates) by the most (or a plurality of) voters is eliminated. BTW, do you know for sure that one of these definitions is incorrect? Obviously the version with the stopping-rule meets your WMW criterion. I am sure that "Arrow-Raynaud" is the same as plain "Raynaud" (sometimes spelt "Reynaud") which is a method that meets the Condorcet criterion. What according to you is its definition, and can you give an example of it failing your WMW criterion? Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] majority winner and range condorcet methods
This from Warren Smith (Tue.Oct.4): Robla failed to mention that range voting *does* obey a weakened form of the majority-winner criterion (call it WMW). Specifically: If a strict majority of the voters regard X as their unique favorite, then they, acting alone without regard to what the other voters do, can force his election. I don't know about you, but I personally regard WMW as a more-desirable critrion for a voting system to obey, than Anderson 1994's MW criterion. Warren, Are there any methods actually *fail* this criterion? Borda perhaps? Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] Andrew Gumbel: Steal this Vote: Dirty Elections and the Rotten History of Democracy in America.
Andrew Gumbel is the LA-based correspondent of the UK paper The Independent. He's written a book,Steal this Vote:Dirty Elections and the Rotten History of Democracy in America, published by Nation Books. If your computer has speakers, you can listen to this RadioNation podcast of him discussing the contents of his book. http://www.podcast.net/show/6336 I found it very interesting. Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] Definition of sincere approval voting (was FBC comparison: WV, margins, MMPO, DMC)
Kevin,
--- Chris Benham [EMAIL PROTECTED] a crit :
This is my proposed clear definition:
"An 'approval vote' is one that makes some approval distinction among
the candidates. It is sincere if
(1)the voter sincerely prefers all the approved candidates (or single
candidate) to all the not approved candidates (or single candidate), and
(2) it is how the voter would vote without any knowledge or guess as to
how other voters might vote."
I have trouble with (2). We could assume that "how the voter would vote"
means optimal, above-mean approval strategy. But obviously that is a
problem for a definition of "sincerity." It would also make approval
satisfy NZIS.
I don't have a big problem with plain Approval satisfying NZIS. Of
course Approval is promoted as a
method that invites voters to strategize.
Otherwise we could choose to not define "how the voter would vote." But
in that case nothing prevents a strategically unwise vote from being
sincere, so that I don't see how DMC could satisfy NZIS.
If , by some absolute standard in the voter's mind, the voter sincerely
"approves" at least one but not all of the candidates
then "sincere approval" is clearcut. I suppose if this isn't the case
then as you say if we leave undefined "how the voter
would vote" there is still 0-info. approval strategy (so plain
Approval doesn't really meet NZIS).
You would have
to claim that DMC has no zero-info approval strategy.
It seems clear that DMC has no zero-info. *ranking* strategy. (Is that
what you meant?) But unless we define "sincere approval"
as "optimal zero-information approval ('strategy')", then DMC
perhaps doesn't fully meet NZIS.
Chris Benham
Election-methods mailing list - see http://electorama.com/em for list info
[EM] Definition of sincere approval voting (was FBC comparison: WV, margins, MMPO, DMC)
Kevin, --- Jobst Heitzig [EMAIL PROTECTED] a crit : We could discuss whether insincere equal ranking for top is more dishonest or whether approving one more candidate is more dishonest... In my opinion, insincere equal ranking is more insincere than approving an additional candidate. I strongly agree with this. "Sincere approval voting" isn't even clearly defined. I've seen one definition that says that as long as the voter sincerely prefers all the candidates s/he approves to all the ones s/he doesn't, then the "approval vote" is sincere. To me this is mainly a bit of sophistry for the purpose of promoting Approval. This is my proposed clear definition: "An 'approval vote' is one that makes some approval distinction among the candidates. It is sincere if (1)the voter sincerely prefers all the approved candidates (or single candidate) to all the not approved candidates (or single candidate), and (2) it is how the voter would vote without any knowledge or guess as to how other voters might vote." By this definition, DMC (like IRV and unlike WV) meets "No Zero-Information Strategy". No method can make it impossible for well-informed strategists to sometimes have an advantage, but it irks me that WV has non-obvious fairly sophisticated strategy for "zero-information" voters (random-fill and if you have a big ratings gap, equal-rank above it). Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] Re: approval strategy in DMC (automated)
Q, I've made a slight change on the DMC page on electowiki. I've extended the definition somewhat: the ballot is a combination of ordinal ranking (equal ranks allowed) and approval rating. The approval rating information can be either binary approval (approved/not-approved) or finer-grained cardinal ratings ([1,0,-1] or [100,99,...,1,0]). I think this is more of a difference in implementation than the method, since the initial ordering is by total approval. In the above case, a more graduated cardinal rating (say 100-0) would allow a voter to approve weaker candidates with a low, but non-zero, rating. Using fine-grained CR ballots with some range like 0 to 100, or even -100 to 100, so that there are always many more possible grades (slots) available than there are candidates allows at the cost of greater counting complexity what is in my opinion a big improvement: (1) Inferring rankings from ratings, eliminate non-members of the Schwartz set. (2) If more than one candidate remains, interpret each ballot to be approving those remaining candidates that it rates higher than the mean of it's ratings of the remaining candidates, and half-approving those that it rates at exactly this mean (and of course not approving those it rates below.) (3) Based on the inferred rankings and the step(2) construed approvals, use Definite Majority Choice (DMC) to elect the winner. The idea is that voters don't need to have any idea of what the chances of any of the candidates being elected are, and voters who (in the manual version) would approve or not approve all the candidates except one sure loser are not unfairly disadvantaged. A while ago I proposed Automated-Approval Margins which is identical except that in step(3) Approval Margins replaces DMC. Also possible would be in step (3) to ignore the rankings and just use (construed) Approval, but at the time I looked at that and decided it wasn't as good on strategy grounds. BTW, I think unadorned DMC with an explicit approval cutoff (so that voters can rank candidates they don't approve) is an excellent practical proposal for public political elections. I am opposed to blindly vote my favourite's ticket idiot boxes (which will just give rich parties incentive to sponsor lots of fake candidates), and to the proposed rule that if some candidate gets more than 66% approval, then the candidate with greatest approval wins. This is an arbitrary complication that would cause the method to fail Majority Favourite and Irrelevant Ballots. Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] Approval variants of MinMax
Forest, You recently wrote on the new Yahoo Condorcet list, beginning by referring to Beatpath, Ranked Pairs, River and MinMax: However, recently Jobst showed that if one measures defeat strength by total approval (of the victor in the pairwise defeat) then all four of these competing methods coalesce into one method. This fact would seem to resolve the controversy unless it turned out that total approval was not a good way to measure defeat strength. However, it seems to be better than winning votes or margins. The defensive properties of winning votes that are normally obtained by defensive truncation can usually (if not always) be obtained by raising the approval cutoff instead of truncating the rankings. Therefore, I suggest that we adopt MinMax(Total Approval) as the Condorcet proposal. Is your first sentence above also true of MinMax (Approval Margins) and the MinMax (Winner's Exclusive Approval)? By the latter I mean measuring the defeat strength by the number of ballots that approve the pairwise winner and not the pairwise loser, as advocated by James Green Armytage. Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] medians and Heitzig's approval-voting strategy
Warren, --aha. So by median candidate you do not mean what I thought you meant (namely, in an N-canddt election, the top-quality floor(N/2) are above median) but rather median in the prior distribution of probabilities of winning. But wait, that would be even more insane, since the policy of voting only for the candidates with above-median prior election probability, would be a policy that would completely disregard the quality of the candidates. My understanding of Weinstein's approval strategy is this: Approve your favourite (or equal favourites). If the remaining (so far unapproved) candidates are on more than one of your preference-levels, then approve the candidate/s on your next-from-the-top preference-level if you consider that the probability that one of the candidates you prefer less than this/these candidate/s will win is greater than the probability that one of the candidates you prefer more will win. And so on. This strategy seems sane to me, and probably right for voters who only have a ranking. Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] question/comments re DMC
Warren, You and Jobst recently had this exchange about Definite Majority Choice (DMC) and Range voting. You begin by quoting one of Jobst's "15 reasons to support DMC". 6. Robustness against "noise" candidates.. cloneproof... WS: --also true of range. JH: Could you say more precisely what you mean here? WS:--Range voting is immune to clones in the sense that any number of cloned candidates, all of whom get the same rangevote scores, can be added to the scene, and the election winner will remain unchanged (except perhaps for replacement by a clone). Also, if "noise" candidates are added who have no hope of winning, then the range votes with noise scores being adjoined for the new candidates, will still yield the same winner and indeed the same totals. Many other voting schemes have these properties (and many also do not have these properties) but in range's case it is particularly self-evident. Range only has this property in a technical sense, in a way that is connected with its technical failure of May's axiom, i.e. it doesn't reduce to FPP when there are only two candidates. Suppose that in the period leading up to the election it is known for sure that two candidates will stand, A and B. A is a left-wing candidate that is hated by big money and its mass media. B is a centre-right candidate that they like. Reliable but perhaps not widely published polls give A52%, B48%. The method to be used in the election is Range, and with just these two candidates standing the voters have no reason not to give maximum points to their preferred candidate and minimum to the other resulting in a solid win for A. How to change B from being the majority loser to the "super-majority consensus candidate"? Easy! A third candidate, C is nominated. C is a horror far-right candidate. Maybe some of A's supporters are members of some ethnic/racial/religious minority that the C candidate says he's in favour of persecuting. Anyway, now all the mass media have to do now is to convince some of A's supporters that C has some chance of winning the election, or just that they should give a maximised sincere vote. So without C we have: 52: A99, B0 48: B99, A0 A wins 5148 to B4752. With C added and some of A's supporters conned and/or frightened, this could become: 47: A99, B0, C0 05: A99, B98, C0 46: B99, A0, C0 02: C99, B98, C0 Now B wins: B5242, A5148, C198. (Approval is also vulnerable to this scenario.) Note that in this example the voted and sincere (binary) pairwise preferences are AB 52-48, AC 52-2, BC 98-2. I think DMC is a very very good (possibly the best) single-winner method to propose for public office elections if we insist on Condorcet and Mono-raise. Chris Benham . Election-methods mailing list - see http://electorama.com/em for list info
[EM] 64 vs 65, post for purpose of annoying Jobst Heitzig
Warren, Incidentlally, since you claim because you cannot explain the precise meaning of a range vote of 64 versus 65, therefore range voting is somehow horribel and inexplicable... and you like DMC... I ask explain to me the precise meaning of `I approve of Bush.' Pretty difficult, isn't it? And also probably strategy dependent - it depends who are Bush's opponents, in practice. All of this is quite analogous to range vote values. (Annoyance mission completed.) wds I dislike plain Approval because it more-or-less forces voters to concern themselves with strategy and the winning probabilities of the candidates. Using a concept of absolute inflexible approval in a method like DOC I used to object to on the same grounds. But now I see that it is mathematically convenient and seems to resonate in the real world. My attempt to precisely define I approve of Bush: If the ballot constrains me to equally help a set of candidates (which I nominate) to defeat any non-member candidates, I put Bush in that set. I prefer Bush to any candidate that I don't approve. Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] Typo: DMC, not DOC
Below is my previous post, corrected: Warren, Incidentlally, since you claim because you cannot explain the precise meaning of a range vote of 64 versus 65, therefore range voting is somehow horribel and inexplicable... and you like DMC... I ask explain to me the precise meaning of `I approve of Bush.' Pretty difficult, isn't it? And also probably strategy dependent - it depends who are Bush's opponents, in practice. All of this is quite analogous to range vote values. (Annoyance mission completed.) wds I dislike plain Approval because it more-or-less forces voters to concern themselves with strategy and the winning probabilities of the candidates. Using a concept of absolute inflexible approval in a method like DMC I used to object to on the same grounds. But now I see that it is mathematically convenient and seems to resonate in the real world. My attempt to precisely define I approve of Bush: If the ballot constrains me to equally help a set of candidates (which I nominate) to defeat any non-member candidates, I put Bush in that set. I prefer Bush to any candidate that I don't approve. Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Center for Range Voting Formed
Adam, You wrote (Fri.Aug.12): * OK, in the interest of fairness, here is one winning-votes Condorcet strategy that is arguably superior to sincerity. This is from Blake Cretney. It's pretty simple: if you have a sincere tied ranking, it's better to rank those candidates in some random order than to rank them equally. So in stead of ranking three candidates tied for fourth, rank them 4, 5, 6, (in some order) and kick any candidates below fourth down two slots. There are situations where this strategy can hurt you, but on average (aggregating over a large number of voters with similar preferences) it will not. I don't think you have that quite right. In the defeat-dropper style winning-votes Condorcet methods you refer to, if the voter sincerely ranks some candidates equal-bottom, then the voter's best zero-information strategy is to strictly rank them all at random (i.e. to random-fill). In addition to that, if above-bottom equal-ranking is allowed, then if the voter has a sufficiently large gap in his/her sincere ratings he/she should equal-rank above that gap. Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
Re: [EM] Re the official definition of condorcet
Warren, You quoted: 1. condorcet.org definitions page: Name: Condorcet Criterion Application: Ranked Ballots Definition: If an alternative pairwise beats every other alternative, this alternative must win the election. Pass: Black, Borda-Elimination, Dodgson, Kemeny-Young, Minmax, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax, Sum of Defeats Fail: Borda, Bucklin, Coombs, IRV And remarked: (Note that, revealingly, they do not consider range voting or plurality voting to either pass or fail.) Maybe you missed Application: Ranked Ballots. Blake Cretney doesn't classify RV or plurality voting (aka FPP) as ranked-ballot methods. He is referring only to methods that reduce to FPP when there are two candidates, so there is no ambiguity about his meaning of pairwise beats. For a method to meet the CC, it must allow the voters to express all their pairwise (binary) preferences or in other words their full ranking. That cuts out FPP, Approval and limited-slot ballot methods with fewer available slots than there are candidates. Then it must elect any candidate that pairwise beats all the others. X pairwise beats Y if more voters rank X above Y than vice versa. No ambiguity that I can see. A Range Voting ballot with many more available slots than there are candidates does allow the voter to give his/her full rankings. It can be regarded as simply a ranked ballot with some extra extraneous ratings information on it. But just because RV uses this extra information, I don't see any need to generalize the CC to accommodate it. This no-hyperlink choice is in fact a plausible way to go because then the condorcet criterion is about the logical self-consistency of a method, as opposed to the consistency of method A as judged using method B, which is kind of an unfair pre-biased way to judge A. Voting methods don't have any feelings or rights, so therefore this alleged unfairness doesn't matter. Chris Benham Election-methods mailing list - see http://electorama.com/em for list info
[EM] Irrelevant Ballots criterion
Participants,
I've come up with a criterion I like, in part inspired by the Blank
Ballot Criterion. As that criterion is currently worded in the Electowiki:
The addition of one or more blank ballots cannot change the winner.
I don't think is very useful because any method can easily dodge it
simply by including a rule that blank ballots aren't counted.
I propose the Independence from Irrelevant Ballots criterion:
If candidate X pairwise loses to all other candidates and is ranked
no higher than equal bottom on all ballots except those that plump for X,
then if ballots that plump for X are deleted the winner must not change.
I think this covers Russ's intention in the way he proposed the Blank
Ballot Criterion:
No method that depends on majority defeats can pass this criterion
if it defines a majority it terms of the total number of voters.
So Irrelevant Ballots can somewhat embarrass CDTT,IRV:
49: A
24: B
27: CB
03: D
(103 ballots)
The CDTT is {ABC} and CDTT,IRV elects A, but if we delete the
irrelevant 3D ballots then A drops out of the CDTT
and the new CDTT,IRV winner is C.
Woodall's Descending Acquiescing Coalitions (DAC) method doesn't use
any majority concept, but in this excellent example from M.Harman (aka
Auros) it stumbles on
Irrelevant Ballots:
03: D
14: A
34: AB
36: CB
13: C
ABCD 100
ABC 97 (eliminate D)
BCD 52 (eliminate A)
AB D 51 (eliminate C, B wins)
DAC elects B, but if we delete the irrelevant 3D ballots then C wins.
A perhaps-more-elegant, stronger version that applies to methods that rank a
candidate last could be called
Strong Independence from Irrelevant Ballots (BTW, I am happy for these to be
abbreviated by dropping the Independence from bit).
Deleting ballots that plump for the candidate ranked last must not change the
winner.
But so far I think the main weak version is more useful. (BTW, plump in this context
means bullet-vote)
Chris Benham
Election-methods mailing list - see http://electorama.com/em for list info
