Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
On Tue, Nov 10, 2009 at 10:52 PM, Kristofer Munsterhjelm wrote: > In the context of SEC, it would be: > > Voter submits two ballots - one is ranked and the other is a Plurality > ballot. Call the first the fallback ballot, and the second the consensus > ballot. > > If everybody (or some very high percentage, e.g. 99%) votes for the same > consensus ballot, it wins. Otherwise, construct a Condorcet matrix based on > the fallback ballots. Pick two candidates at random and the one that > pairwise beats the other, wins. How do you pick the random candidates? For that to be clone independent, there would actually need to be 3 ballots: - consensus ballot If more than X% of the ballots pick the same candidate, then that candidate wins. - nomination ballot - fallback ranking 2 nomination ballots are picked to decide the candidate and the pairwise winner according to the rankings wins. However, as I said in my last post, the nomination ballot isn't strategy free. > To my knowledge, Random Pair is strategy-free. It might also be > proportional, but I'm not sure about that (partly because I'm not sure how > you'd define "proportional" for ranked ballots). The problem is picking the 2 candidates. If 2 are picked at random, then the method isn't clone independent. Also, it favours the condorcet winner, so may suffer from tyranny of the majority. However, if you had a divided society, then both ethnic groups would still have some say. For example, if the split was 55% (A) and 45 (B), and each ethnic group only voted for their own candidate, then the results would be 2 A's: 30% => ethnic group A wins A+B: 50% => ethnic group A wins (as they are the majority) 2 B's: 20% => ethnic group B wins Thus group B gets some power, but not proportional power. However, once the society starts working better, it would seamlessly transition to a near condorcet method. Also, in a divided society condorcet voting might reduce the issue directly. In both cases, there would be an incentive for politicians from ethnic group A to try to get support from voters in ethnic group B. OTOH, a random election method may not be the best plan in a society where corruption is a problem. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Raph Frank wrote: On Tue, Nov 10, 2009 at 8:11 PM, Jobst Heitzig wrote: Hello Kristofer, Assume (for the sake of simplicity) that we can get ranked information from the voters. What difference would a SEC with Random Pair make, with respect to Random Ballot? This sounds interesting, but what exactly do you mean by Random Pair? Pick a randomly chosen pair of candidates and elect the pairwise winner of them? I will think about this... Presumably, it means that the voter submits 2 ballots, a ranking and a nomination for the 2nd round? In the context of SEC, it would be: Voter submits two ballots - one is ranked and the other is a Plurality ballot. Call the first the fallback ballot, and the second the consensus ballot. If everybody (or some very high percentage, e.g. 99%) votes for the same consensus ballot, it wins. Otherwise, construct a Condorcet matrix based on the fallback ballots. Pick two candidates at random and the one that pairwise beats the other, wins. To my knowledge, Random Pair is strategy-free. It might also be proportional, but I'm not sure about that (partly because I'm not sure how you'd define "proportional" for ranked ballots). You seem to be suggesting a more Condorcet way of doing the consensus balloting. A possible option would be to look at how e.g. Debian handles supermajority issues. On the other hand, grafting Condorcet onto the consensus option would make the actual consensus more opaque, and one may in any case argue: "if you have a consensus, there's an agreement and so you don't need a complex method to determine what the consensus actually is". Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
On Tue, Nov 10, 2009 at 8:11 PM, Jobst Heitzig wrote: > Hello Kristofer, >> Assume (for the sake of simplicity) that we can get ranked information >> from the voters. What difference would a SEC with Random Pair make, with >> respect to Random Ballot? > > This sounds interesting, but what exactly do you mean by Random Pair? > Pick a randomly chosen pair of candidates and elect the pairwise winner > of them? I will think about this... Presumably, it means that the voter submits 2 ballots, a ranking and a nomination for the 2nd round? Clearly, your rankings should be honest, as it is only looked at once the 2 candidates have been decided. However, your nomination would have to be made tactically. It would require that the voter decide the probability of the candidate they nominate winning. If you nominate the condorcet winner, then the odds of your candidate winning the second round is 100%, as no other candidate can possibly beat him.. However, if you nominate an extremist, then your nomination is almost certain to fail, as he will lose to virtually any other candidate. If the voter distribution is symmetric (and voter utility is symmetric) around a central point, then the nominated candidate who is closest to the centre will win. If each voter nominates their favourite, then you best strategy is to nominate the the candidate which maximises f(distance)*utility f(distance) is the fraction of the nominations that nominate candidates further away than that distance from the centre. f(0) is automatically 1 and f(most extremist candidate's distance) is automatically 0. Also, f(d) is a monotonic decreasing function. Thus, when considering 2 candidates of near equal utility, you should nominate the candidate nearest the centre. However, if all voters do that, then most of the nominations will start to be clustered near the centre. This means that the voters should nominate candidates even closer to the centre. I.e. if f(d) = 0.1, then you would have to prefer that candidate at least 10 times better than the condorcet winner in order to nominate him. I think the effect could very easily end up being that the condorcet winner normally wins. It could also be implemented in 2 formal rounds. In the first round, each voter votes for 1 candidate. 2 candidates are picked at random, using random ballot. Those 2 candidates then proceed to the run off. This might even make people accept random ballot. The problem that a candidate with 1% support could get to be President is eliminated. (Unless it happens twice in 1 election.) Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] About non-monotonicity and non-responding to previous posts...
What I wrote last time is about as simple as you get. Canceling the smallest margin cancels a three-member cycle, leaving the strongest member as CW. Could take more canceling for more complex, and thus rarer, cycles. Dave Ketchum On Nov 10, 2009, at 7:54 AM, Kristofer Munsterhjelm wrote: Dave Ketchum wrote: Trying some fresh thinking for Condorcet, and what anyone should be able to see in the X*X array. I am ignoring labels such as Schulze and Ranked Pairs - this is human-doable and minimal effort - especially with normally having a CW and most cycles having the minimal three members. 1. Look at any pair of candidates. Loser is not the CW (there can be a tie in any comparison here - NOT likely in a normal election, but we have to be prepared with responses for such). 2. If there are other possible CWs, repeat step 1 with latest winner and one of them. 3. If there are other candidates latest winner has not been compared with, compare it with each of them. 4. If winner wins each of these, it is CW. 5. Winner and each who beat it in step 4 are cycle members. Also, any candidate beating any of these is also a cycle member. IF there is a CW, it should win - anything else is a complication, even if some math makes claims for the something else. Otherwise a simple cycle resolution should apply. Simply canceling the smallest margin has been thought of - that value means minimum difference in vote counts between actual and what is assumed. Note that each cycle member would be CW if remaining cycle members were ignored. As to voting: Equal ranks permitted. Write-ins permitted, and such a candidate wins with the same vote counts as if nominated. As to clones, strategy, primaries, and runoffs - all seem best ignored, though only a nuisance if some are determined to involve such. Okay, so let's see which *simple* cycle breaker provides as much as possible. To do that, we'll need to find out what simplicity means, and how to define "as much as possible". That could be interesting in itself. Ranked Pairs (or River) seems nice, but even it may be too complex. Sports usually employ Copeland (but modified); perhaps that could be used - but Copeland is indecisive. One can add Smith compliance by checking for a CW among the first n ranked in the output, then n-1, then n-2 and so on, but that might also be too complex. Of course, if simplicity is paramount (i.e. we want very simple) we could just go with "break it by whoever beats the Plurality winner by the greatest amount" or plain old minmax (candidate with least worst defeat wins) or LR (greatest sum of victories wins). Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Jobst Heitzig wrote: Hello Kristofer, you wrote: You could probably devise a whole class of SEC-type methods. They would go: if there is a consensus (defined in some fashion), then it wins - otherwise, a nondeterministic strategy-free method is used to pick the winner. The advantage of yours is that it uses only Plurality ballots. The hard point is, I think, to define what actually a potential consensus option is. And here the idea was to say everything unanimously preferred to some benchmark outcome qualifies as potential consensus. The benchmark then cannot be any feasible option but must be a lottery of some options, otherwise the supporters of the single option would block the consensus. But which lottery you take as a benchmark could be discussed. I chose the Random Ballot lottery since it seems the most fair one and has all nice properties (strategy-freeness, proportional allocation of power). I suppose the nondeterministic method would have to be "bad enough" to provide incentive to pick the right consensus, yet it shouldn't be so bad as to undermine the process itself if the voters really can't reach a consensus. Although I can hardly imagine real-world situations in which no consensus option can be found (maybe be combining different decisions into one, or using some kind of compensation scheme if necessary). That might be true for a consensus in general, but I was referring to the SEC method, where all it takes is for a single voter to submit a different consensus ballot than the rest. Assume (for the sake of simplicity) that we can get ranked information from the voters. What difference would a SEC with Random Pair make, with respect to Random Ballot? This sounds interesting, but what exactly do you mean by Random Pair? Pick a randomly chosen pair of candidates and elect the pairwise winner of them? I will think about this... Yes. The CW now has a greater chance to win - but note that it's not given that the CW will win, because if he's not picked as one of the pair candidates, he doesn't come into play at all. It would lead to a better outcome if the consensus fails, but so also make it more likely that the consensus does fail. Or would it? The reasoning from a given participant's point of view is rather: do I get something *I* would like by refusing to take part in consensus -- not, does *society* get something acceptable. I'm not sure I know what you mean here. Well, I was thinking that the SEC method provides an incentive for people to reach a common consensus because the alternative, which is the random ballot, isn't very good. Any (random or deterministic) method that favors some group would lead to that group having less of an incentive to participate in the consensus process because they know they'll get something they'll like. Therefore, I at first thought that even though Random Pair would provide a result more people would be happy with, it would make the voters less interested in actually finding a consensus because the alternative isn't so bad anymore. However, then I realized that any given voter, if he's at the point where he doesn't care about the consensus option, will not be deterred from such a line of thinking because the alternative is suboptimal for society, only if it is suboptimal in his point of view. That means that you could replace Random Ballot with Random Pair as long as the fairness (what you call proportional allocation of power) remains intact, because if the improvement in result lifts all the groups equally, there's no more incentive for some group to "cheat" with respect to any other. There's also another way of looking at it, which I just saw now: my first idea was that you can't move to a lottery that gives consistently good results because that will diminish people's interest in determining a consensus. But if the lottery is both fair and provides good results, then who cares? The consensus option will only come into play if the people can explicitly agree on a choice that's better than the expected value of the lottery. If figuring out a consensus is worth it (much better than the lottery, relatively speaking), then people will care, otherwise they won't. Thus improving the lottery part of the method will improve the method in general - it'll make up the amount it no longer encourages people to determine the consensus, by just giving better results. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Hello Kristofer, you wrote: > However, my point was that Range goes further: a minority that acts > in a certain way can get what it wants, too; all that's required is that > the majority does not vote Approval style (either max or min) and that > the minority does, and that the minority is not too small. > > It is in that respect I mean that Range is more radical, because it > permits a minority to overrule a majority that otherwise agrees about > which candidates it prefers. For those who mean that elections have to > be, at least, majoritarian, Range may contain a surprise. That's true. Methods in which a group can suppress the rest are certainly bad, even more so when the group can be small... > You could probably devise a whole class of SEC-type methods. They would > go: if there is a consensus (defined in some fashion), then it wins - > otherwise, a nondeterministic strategy-free method is used to pick the > winner. The advantage of yours is that it uses only Plurality ballots. The hard point is, I think, to define what actually a potential consensus option is. And here the idea was to say everything unanimously preferred to some benchmark outcome qualifies as potential consensus. The benchmark then cannot be any feasible option but must be a lottery of some options, otherwise the supporters of the single option would block the consensus. But which lottery you take as a benchmark could be discussed. I chose the Random Ballot lottery since it seems the most fair one and has all nice properties (strategy-freeness, proportional allocation of power). > I suppose the nondeterministic method would have to be "bad enough" to > provide incentive to pick the right consensus, yet it shouldn't be so > bad as to undermine the process itself if the voters really can't reach > a consensus. Although I can hardly imagine real-world situations in which no consensus option can be found (maybe be combining different decisions into one, or using some kind of compensation scheme if necessary). > Assume (for the sake of simplicity) that we can get ranked information > from the voters. What difference would a SEC with Random Pair make, with > respect to Random Ballot? This sounds interesting, but what exactly do you mean by Random Pair? Pick a randomly chosen pair of candidates and elect the pairwise winner of them? I will think about this... > It would lead to a better outcome if the > consensus fails, but so also make it more likely that the consensus does > fail. Or would it? The reasoning from a given participant's point of > view is rather: do I get something *I* would like by refusing to take > part in consensus -- not, does *society* get something acceptable. I'm not sure I know what you mean here. Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval andrange voting? (long)
On Nov 10, 2009, at 7:58 AM, Matthew Welland wrote: On Tuesday 10 November 2009 03:57:34 am you wrote: Dear Matthew, you wrote: Suite of complicated systems that strive to reach "Condorcet" ideals. 1. No regular bloke would ever trust 'em because you can't explain how they work in one or two sentences. Well, here's a very simple "Condorcet" system which can easily be explained in two sentences: 1. Let voters vote on candidate pairs, successively replacing the loser with a different candidate, in a random order of candidates. 2. As soon as all candidates have been included, the winner of the last pair is declared the overall winner. This system is arguably the earliest example of a "Condorcet" system. It was devised by Ramon Llull in the 13th century and was successfully used for elections in monastaries. It is easily understood by the common man since it resembles a procedure frequently used in child play. That is an excellent description. Thanks. Gives a feel for something good enough for their purposes - if there is a CW the CW wins. BUT, if there is a cycle, the best candidate can lose to another cycle member - so better make sure the apparent CW gets compared with every other candidate. I've always liked that specific system and think being Condorcet compliant makes great sense in smaller elections or where a perfect choice is critical. Implementing it on a large scale seems tough and actually voting in it seems tedious. If there are N candidates am I forced to make N-1 decisions? If there is a short circuit way to do the vote then it might be workable. In voting you could start with thinking who you would approve of. Then vote for them, while ignoring the others that you like less. Do any of: Approve them by giving them the same rank. Vote for the best as in FPTP. Rank them to show your preference for better vs lesser. The improvement over approval still seems marginal, especially in large elections and I think the cost for implementing, tabulating and voting is much higher, Agreed the implementing costs - mostly in being able to do this. With the ability you get a big help in some elections and less or little in others (like 0 when only two candidates). Tabulating a ballot gets to be labor when a voter ranks many candidates. Being able to determine winner from the N*N array was an implementing cost, but then easy to do via computer (assuming use of an easy variant of Condorcet). Voters who were happy with FPTP will see no benefit - but no cost once they see they can vote as they have before. Voters who have studied range/score will make two groups: sad to be unable to express the exact size of their likes/dislikes; thankful for the easier decisions involved here. Voters who want to rank higher those they like best will be thankful to get past approval. Dave Ketchum Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] NESD and NESD* properties of a single-winner voting method
Let me clarify my thinking a bit (I hope) behind NESD and NESD*. NESD stands for "Naive Exaggeration Strategy ==> Duopoly." NES means the voter strategy of 1) identify the "top two" candidates most likely to win. 2) Exaggerate your (otherwise honest) vote to rank one top and the other bottom. (With NESD*, unique-top; with NESD, permitted to be co-equal top.)It appears that, in the real world, this is a pretty close approximation of what a very large percentage of voters in large well publicized+polled elections actually do (it does not necessarily always make complete sense that they do that, but the data indicates they do it anyway). The D part means: if all (or a very large percentage) of voters exhibit NES behavior, then one of the top-two will always win (except in exceedingly unlikely "perfect-tie" scenarios). And in fact, the same winner will arise as in strategic plurality voting, so any system failing NESD or NESD* can be accused (perhaps not with full justification, but certainly with some) of being "equivalent in the real world" to plain plurality voting, and presumably leading of historical time to "duopoly" where voters effectively only get one of two choices every election. This severely diminishes voter choice and "democracy" if it happens (versus some system with more than 2 choices). It's an interesting property (or two properties) and I think worth consideration. You can now ask yourself other interesting questions, like "how can I design good voting systems passing NESD or NESD*?" etc. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] NESD and NESD* properties of a single-winner voting method
On Nov 10, 2009, at 5:07 AM, Kristofer Munsterhjelm wrote: > Jobst Heitzig wrote: >> Dear Warren, >> I don't seem to understand the definition: >>> A single-winner voting system "fails the NESD property" if, when every >>> honest voter >>> changes their vote to rank A top and B bottom (or B top and A bottom; >>> depends on the voter which way she goes), leaving it otherwise >>> unaltered, that always (except in very rare "exact tie" situations) >>> causes A or B to win. >> So, when all voters vote strategic (i.e. no voter is honest) and all >> leave their ballots unchanged, then by definition "every honest voter >> changes their vote to rank A top and B bottom" but of course no system >> changes the result since no ballot is changed. Hence no system fails NESD. >> What is the misunderstanding here? > > I think he means: > > Call the first group of ballots, X, consisting of ranked ballots made by > honest voters. Now take every ballot in X and, for each ballot y, if y votes > A > B, put A first and B last, or if y votes B > A, put B first and A last, > leavin the ballot otherwise unchanged. Call the modified bundle, consisting > of these modified y-ballots, X'. > > If there exists such a group of ballots X so that the method in question > gives a different victor when fed X and when fed X', and gives either A or B > as the victor for group X', then it fails the NESD property. > > In other words: if the entire electorate decides that the dangerous contest > is A vs B and so maximally buries the one they like the least, and this > strategy pays off, then it fails this property. That's the way I read it. In other words, interpret Majority failure as a virtue. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting?
Jobst Heitzig wrote: Dear Kristofer, both Approval Voting and Range Voting *are* majoritarian: A majority can always get their will and suppress the minority by simply bullet-voting. So, a more interesting version of your question could be: Which *democratic* method (that does not allow any sub-group to suppress the rest) has (usually or on average or in the worst case) the least Bayesian Regret. Yes. A majority that acts in a certain way can get what it wants. That's true for Range and Approval, and it's true for Condorcet, Plurality, etc. However, my point was that Range goes further: a minority that acts in a certain way can get what it wants, too; all that's required is that the majority does not vote Approval style (either max or min) and that the minority does, and that the minority is not too small. It is in that respect I mean that Range is more radical, because it permits a minority to overrule a majority that otherwise agrees about which candidates it prefers. For those who mean that elections have to be, at least, majoritarian, Range may contain a surprise. I conjecture that at least when the nomination of additional options is allowed, the method SEC described recently is a hot candidate for this award, since it seems that SEC will lead to the election of the option at the *mean* (instead of the median) voter position, and I guess that in most spacial utility models the mean position is in many senses "better" and will in particular have less Bayesian Regret than the median position. (Recall that in a one-dimensional spacial model where additional options can be nominated, all majoritarian methods likely lead to median positions being realized and are thus basically all equivalent.) You could probably devise a whole class of SEC-type methods. They would go: if there is a consensus (defined in some fashion), then it wins - otherwise, a nondeterministic strategy-free method is used to pick the winner. The advantage of yours is that it uses only Plurality ballots. I suppose the nondeterministic method would have to be "bad enough" to provide incentive to pick the right consensus, yet it shouldn't be so bad as to undermine the process itself if the voters really can't reach a consensus. Assume (for the sake of simplicity) that we can get ranked information from the voters. What difference would a SEC with Random Pair make, with respect to Random Ballot? It would lead to a better outcome if the consensus fails, but so also make it more likely that the consensus does fail. Or would it? The reasoning from a given participant's point of view is rather: do I get something *I* would like by refusing to take part in consensus -- not, does *society* get something acceptable. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] NESD and NESD* properties of a single-winner voting method
Jobst Heitzig wrote: Dear Warren, I don't seem to understand the definition: A single-winner voting system "fails the NESD property" if, when every honest voter changes their vote to rank A top and B bottom (or B top and A bottom; depends on the voter which way she goes), leaving it otherwise unaltered, that always (except in very rare "exact tie" situations) causes A or B to win. So, when all voters vote strategic (i.e. no voter is honest) and all leave their ballots unchanged, then by definition "every honest voter changes their vote to rank A top and B bottom" but of course no system changes the result since no ballot is changed. Hence no system fails NESD. What is the misunderstanding here? I think he means: Call the first group of ballots, X, consisting of ranked ballots made by honest voters. Now take every ballot in X and, for each ballot y, if y votes A > B, put A first and B last, or if y votes B > A, put B first and A last, leavin the ballot otherwise unchanged. Call the modified bundle, consisting of these modified y-ballots, X'. If there exists such a group of ballots X so that the method in question gives a different victor when fed X and when fed X', and gives either A or B as the victor for group X', then it fails the NESD property. In other words: if the entire electorate decides that the dangerous contest is A vs B and so maximally buries the one they like the least, and this strategy pays off, then it fails this property. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval andrange voting? (long)
On Tuesday 10 November 2009 03:57:34 am you wrote: > Dear Matthew, > > you wrote: > > Suite of complicated systems that strive to reach "Condorcet" ideals. > > > >1. No regular bloke would ever trust 'em because you can't explain > > how they work in one or two sentences. > > Well, here's a very simple "Condorcet" system which can easily be > explained in two sentences: > > 1. Let voters vote on candidate pairs, successively replacing the loser > with a different candidate, in a random order of candidates. > 2. As soon as all candidates have been included, the winner of the last > pair is declared the overall winner. > > This system is arguably the earliest example of a "Condorcet" system. It > was devised by Ramon Llull in the 13th century and was successfully used > for elections in monastaries. It is easily understood by the common man > since it resembles a procedure frequently used in child play. That is an excellent description. Thanks. I've always liked that specific system and think being Condorcet compliant makes great sense in smaller elections or where a perfect choice is critical. Implementing it on a large scale seems tough and actually voting in it seems tedious. If there are N candidates am I forced to make N-1 decisions? If there is a short circuit way to do the vote then it might be workable. The improvement over approval still seems marginal, especially in large elections and I think the cost for implementing, tabulating and voting is much higher, > Yours, Jobst > > Matthew Welland schrieb: > > Thanks all for the discussion and pointers. I still can't concretely > > conclude anything yet but here are some rambling and random thoughts > > based on what was said and my prior experiences. > > > > Plurality > > > >1. Leads to two lowest common denominator parties which are not > > accountable to the voters. This conclusion supported by real > > world observation. > >2. Feels right to the non-critical mind, "one man, one vote" > >3. Very fast at the polls > > > > Approval > > > >1. Encourages participation of minor parties and thus should keep > > the big guys paying attention to a wider base. > >2. Almost zero marginal implementation cost. Hanging chads count > > just fine :) > >3. Understandable by anyone but feels wrong at first "not fair, you > > get more than one vote". > >4. Apparently has a terrible flaw but no one seems to be able to > > articulate it in layman terms. No real world experience available > > to illustrate the problem. Here is where I need to learn more. > > Data provided to date is unconvincing to me. > >5. Does not meet the desire of some to be able to differentiate > > between "I like", "I like a lot" etc. (note: this seems like > > perfectionism to me. Large numbers of voters and opinions all > > over the bell curve should make individual expression at the greater > > level of granularity irrelevant.) > >6. Very fast at the polls. Pick yer favorites and head home for beer > > and telly. > > > > Range > > > >1. Can break the vicious cycle of plurality > >2. Not voting for someone at all can have a strong influence on > > election outcome. This is very non-intuitive and would take some > > getting used to. > >3. Allows for nuanced voting. > >4. Pain in the ass at the polls (relatively speaking). You can't > > safely disregard the candidates you don't care about so you > > *have* to assign everyone a ranking, possibly addressable by defaulting > > to zero for all candidates? This is considered a feature and I agree it > > has merit. But in reality it is a deal breaker for joe six pack and co. > > (and for lazy sobs like me). > > > > IRV > > > >1. Demonstrably broken. 'nuff said. > > > > Suite of complicated systems that strive to reach "Condorcet" ideals. > > > >1. No regular bloke would ever trust 'em because you can't explain > > how they work in one or two sentences. > >2. Technically superior to other systems. > >3. Not clear what problem with approval they would solve. Unless you > > are a perfectionist and insist that individuals express nuances > > of opinion... > > > > Some time ago I put together a site (primitive and unfinished[i]) to > > promote approval voting and in the process I spent a lot of time trying > > different systems on the web and repeatedly testing my own site. I > > noticed some interesting things from all that playing around. > > > >1. It was very uncomfortable to go back to plurality after trying > > other systems. It "feels" unfair and broken. > >2. It was very tedious voting in any of the ranking systems. > >3. Approval felt boring but good. > > > > I have checked in on this list now and then and I admit I don't have > > the time or skills to follow all the arguments but it strikes me that > > approval voting is good enough to break the deadlock, at least i
Re: [EM] About non-monotonicity and non-responding to previous posts...
Dave Ketchum wrote: Trying some fresh thinking for Condorcet, and what anyone should be able to see in the X*X array. I am ignoring labels such as Schulze and Ranked Pairs - this is human-doable and minimal effort - especially with normally having a CW and most cycles having the minimal three members. 1. Look at any pair of candidates. Loser is not the CW (there can be a tie in any comparison here - NOT likely in a normal election, but we have to be prepared with responses for such). 2. If there are other possible CWs, repeat step 1 with latest winner and one of them. 3. If there are other candidates latest winner has not been compared with, compare it with each of them. 4. If winner wins each of these, it is CW. 5. Winner and each who beat it in step 4 are cycle members. Also, any candidate beating any of these is also a cycle member. IF there is a CW, it should win - anything else is a complication, even if some math makes claims for the something else. Otherwise a simple cycle resolution should apply. Simply canceling the smallest margin has been thought of - that value means minimum difference in vote counts between actual and what is assumed. Note that each cycle member would be CW if remaining cycle members were ignored. As to voting: Equal ranks permitted. Write-ins permitted, and such a candidate wins with the same vote counts as if nominated. As to clones, strategy, primaries, and runoffs - all seem best ignored, though only a nuisance if some are determined to involve such. Okay, so let's see which *simple* cycle breaker provides as much as possible. To do that, we'll need to find out what simplicity means, and how to define "as much as possible". That could be interesting in itself. Ranked Pairs (or River) seems nice, but even it may be too complex. Sports usually employ Copeland (but modified); perhaps that could be used - but Copeland is indecisive. One can add Smith compliance by checking for a CW among the first n ranked in the output, then n-1, then n-2 and so on, but that might also be too complex. Of course, if simplicity is paramount (i.e. we want very simple) we could just go with "break it by whoever beats the Plurality winner by the greatest amount" or plain old minmax (candidate with least worst defeat wins) or LR (greatest sum of victories wins). Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting? (long)
On Tuesday 10 November 2009 03:37:56 am Kristofer Munsterhjelm wrote:
> Matthew Welland wrote:
> > So, to re-frame my question. What is the fatal flaw with approval? I'm
> > not interested in subtle flaws that result in imperfect results. I'm
> > interested in flaws that result in big problems such as those we see
> > with plurality and IRV.
>
> IMHO, it is that you need concurrent polling in order to consistently
> elect a good winner. If you don't have polling and thus don't know where
> to put the cutoff (between approve and not-approve), you'll face the
> Burr dilemma: If you prefer A > B > C, if you "approve" both A and B,
> you might get B instead of A, but if you "approve" only A, you might get
> C!
This seems to me to be a minor, not major, flaw. Having to vote A & B to
hedge your bets is not ideal but you might even be able to argue some
benefits to it. A will see B as a serious threat and vice versa. They may
make adjustments to their stands on issues to accommodate voters like you.
Approval voting is enough to bring competition for votes back into the arena
and I think it makes negative campaigning a very risky strategy.
Also, again, your single vote is irrelevant. It is the aggregate of
thousands or millions of votes that will make or break A vs. B. How many
feel so strongly against A that they cannot vote for him or her?
The binary nature of approval is washed out by large numbers just as a class
D amplifier can directly produce smooth analog waveforms out of a pure 1 or 0
signal.
> Thus the kind of Approval that homes in on a good winner employs
> feedback. The method is no longer Approval alone, but Approval plus
> polling. That /can/ work (people approve {Nader, Gore} if Nader has
> fewer votes than Gore, so that Bush doesn't win from the split, but only
> approve either Nader or Gore if both are large), but why should we need
> to be burdened with the feedback?
Sure, in any real election there will be many dynamics at work. Feedback
polls, debates etc. will all improve an election. Approval might benefit from
feedback but I don't see why it becomes fatally flawed without it, only
mildly flawed.
> Some, like Abd, argue that we always reason based on others' positions
> to know how much we can demand, and so that this is a feature rather
> than a bug. That doesn't quite sound right to me. In any event, if you
> want Approval + bargaining (which the feedback resolves to), make that
> claim. Approval alone, without feedback, will be subject to the flaws
> mentioned earlier, however.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval and range voting? (long)
On Tue, Nov 10, 2009 at 10:37 AM, Kristofer Munsterhjelm wrote: > IMHO, it is that you need concurrent polling in order to consistently elect > a good winner. If you don't have polling and thus don't know where to put > the cutoff (between approve and not-approve), you'll face the Burr dilemma: > If you prefer A > B > C, if you "approve" both A and B, you might get B > instead of A, but if you "approve" only A, you might get C! However, the same logic can be applied to plurality voting. If people had to vote blind, then the results would be even worse. History with plurality has shown that it is reasonable to expect people to know who the top-2 candidates are. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval andrange voting? (long)
This method is also quite hand countable (unlike many other Condorcet methods). That was certainly an important feature in those days :-). It has some randomness in the results (when no Condorcet winner exists). Here's another one. Elect the candidate that wins all others in pairwise comparisons. If there is no such candidate, elect the one that needs least number of additional votes to win all others. (This is of course the famous minmax(margins) that I have promoted quite often.) Juho On Nov 10, 2009, at 12:57 PM, Jobst Heitzig wrote: Dear Matthew, you wrote: Suite of complicated systems that strive to reach "Condorcet" ideals. 1. No regular bloke would ever trust 'em because you can't explain how they work in one or two sentences. Well, here's a very simple "Condorcet" system which can easily be explained in two sentences: 1. Let voters vote on candidate pairs, successively replacing the loser with a different candidate, in a random order of candidates. 2. As soon as all candidates have been included, the winner of the last pair is declared the overall winner. This system is arguably the earliest example of a "Condorcet" system. It was devised by Ramon Llull in the 13th century and was successfully used for elections in monastaries. It is easily understood by the common man since it resembles a procedure frequently used in child play. Yours, Jobst Matthew Welland schrieb: Thanks all for the discussion and pointers. I still can't concretely conclude anything yet but here are some rambling and random thoughts based on what was said and my prior experiences. Plurality 1. Leads to two lowest common denominator parties which are not accountable to the voters. This conclusion supported by real world observation. 2. Feels right to the non-critical mind, "one man, one vote" 3. Very fast at the polls Approval 1. Encourages participation of minor parties and thus should keep the big guys paying attention to a wider base. 2. Almost zero marginal implementation cost. Hanging chads count just fine :) 3. Understandable by anyone but feels wrong at first "not fair, you get more than one vote". 4. Apparently has a terrible flaw but no one seems to be able to articulate it in layman terms. No real world experience available to illustrate the problem. Here is where I need to learn more. Data provided to date is unconvincing to me. 5. Does not meet the desire of some to be able to differentiate between "I like", "I like a lot" etc. (note: this seems like perfectionism to me. Large numbers of voters and opinions all over the bell curve should make individual expression at the greater level of granularity irrelevant.) 6. Very fast at the polls. Pick yer favorites and head home for beer and telly. Range 1. Can break the vicious cycle of plurality 2. Not voting for someone at all can have a strong influence on election outcome. This is very non-intuitive and would take some getting used to. 3. Allows for nuanced voting. 4. Pain in the ass at the polls (relatively speaking). You can't safely disregard the candidates you don't care about so you *have* to assign everyone a ranking, possibly addressable by defaulting to zero for all candidates? This is considered a feature and I agree it has merit. But in reality it is a deal breaker for joe six pack and co. (and for lazy sobs like me). IRV 1. Demonstrably broken. 'nuff said. Suite of complicated systems that strive to reach "Condorcet" ideals. 1. No regular bloke would ever trust 'em because you can't explain how they work in one or two sentences. 2. Technically superior to other systems. 3. Not clear what problem with approval they would solve. Unless you are a perfectionist and insist that individuals express nuances of opinion... Some time ago I put together a site (primitive and unfinished[i]) to promote approval voting and in the process I spent a lot of time trying different systems on the web and repeatedly testing my own site. I noticed some interesting things from all that playing around. 1. It was very uncomfortable to go back to plurality after trying other systems. It "feels" unfair and broken. 2. It was very tedious voting in any of the ranking systems. 3. Approval felt boring but good. I have checked in on this list now and then and I admit I don't have the time or skills to follow all the arguments but it strikes me that approval voting is good enough to break the deadlock, at least in US politics and that it doesn't have any major flaws. The very understandable desire to be able to articulate in a finer grained way in your vote is perfectionism. With millions of voters, for every person on the fence about a particular candidate there will be some to either side who will essentially make or break the vote
Re: [EM] Anyone got a good analysis on limitations of approval andrange voting? (long)
Dear Robert, you wrote: > Round Robin tournament, Ranked Ballot: The contestant who wins in a > single match is the candidate who is preferred over the other in more > ballots. The candidate who is elected to office is the contestant who > loses to no one in the round robin tournament. > > that's two sentences and two labels. But it's incomplete as well... Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval andrange voting? (long)
Dear Matthew, you wrote: > Suite of complicated systems that strive to reach "Condorcet" ideals. > >1. No regular bloke would ever trust 'em because you can't explain > how they work in one or two sentences. Well, here's a very simple "Condorcet" system which can easily be explained in two sentences: 1. Let voters vote on candidate pairs, successively replacing the loser with a different candidate, in a random order of candidates. 2. As soon as all candidates have been included, the winner of the last pair is declared the overall winner. This system is arguably the earliest example of a "Condorcet" system. It was devised by Ramon Llull in the 13th century and was successfully used for elections in monastaries. It is easily understood by the common man since it resembles a procedure frequently used in child play. Yours, Jobst Matthew Welland schrieb: > Thanks all for the discussion and pointers. I still can't concretely > conclude anything yet but here are some rambling and random thoughts > based on what was said and my prior experiences. > > Plurality > >1. Leads to two lowest common denominator parties which are not > accountable to the voters. This conclusion supported by real world > observation. >2. Feels right to the non-critical mind, "one man, one vote" >3. Very fast at the polls > > Approval > >1. Encourages participation of minor parties and thus should keep the > big guys paying attention to a wider base. >2. Almost zero marginal implementation cost. Hanging chads count just > fine :) >3. Understandable by anyone but feels wrong at first "not fair, you > get more than one vote". >4. Apparently has a terrible flaw but no one seems to be able to > articulate it in layman terms. No real world experience available > to illustrate the problem. Here is where I need to learn more. > Data provided to date is unconvincing to me. >5. Does not meet the desire of some to be able to differentiate > between "I like", "I like a lot" etc. (note: this seems like > perfectionism to me. Large numbers of voters and opinions all over > the bell curve should make individual expression at the greater > level of granularity irrelevant.) >6. Very fast at the polls. Pick yer favorites and head home for beer > and telly. > > Range > >1. Can break the vicious cycle of plurality >2. Not voting for someone at all can have a strong influence on > election outcome. This is very non-intuitive and would take some > getting used to. >3. Allows for nuanced voting. >4. Pain in the ass at the polls (relatively speaking). You can't > safely disregard the candidates you don't care about so you *have* > to assign everyone a ranking, possibly addressable by defaulting > to zero for all candidates? This is considered a feature and I > agree it has merit. But in reality it is a deal breaker for joe > six pack and co. (and for lazy sobs like me). > > IRV > >1. Demonstrably broken. 'nuff said. > > Suite of complicated systems that strive to reach "Condorcet" ideals. > >1. No regular bloke would ever trust 'em because you can't explain > how they work in one or two sentences. >2. Technically superior to other systems. >3. Not clear what problem with approval they would solve. Unless you > are a perfectionist and insist that individuals express nuances of > opinion... > > Some time ago I put together a site (primitive and unfinished[i]) to > promote approval voting and in the process I spent a lot of time trying > different systems on the web and repeatedly testing my own site. I > noticed some interesting things from all that playing around. > >1. It was very uncomfortable to go back to plurality after trying > other systems. It "feels" unfair and broken. >2. It was very tedious voting in any of the ranking systems. >3. Approval felt boring but good. > > I have checked in on this list now and then and I admit I don't have the > time or skills to follow all the arguments but it strikes me that > approval voting is good enough to break the deadlock, at least in US > politics and that it doesn't have any major flaws. The very > understandable desire to be able to articulate in a finer grained way in > your vote is perfectionism. With millions of voters, for every person on > the fence about a particular candidate there will be some to either side > who will essentially make or break the vote. If you are on the fence, > approve or disapprove, it won't matter. > > So, to re-frame my question. What is the fatal flaw with approval? I'm > not interested in subtle flaws that result in imperfect results. I'm > interested in flaws that result in big problems such as those we see > with plurality and IRV. > > > [i] www.approvalvote.org > > > > -
Re: [EM] Anyone got a good analysis on limitations of approval and range voting? (long)
Matthew Welland wrote:
So, to re-frame my question. What is the fatal flaw with approval? I'm
not interested in subtle flaws that result in imperfect results. I'm
interested in flaws that result in big problems such as those we see
with plurality and IRV.
IMHO, it is that you need concurrent polling in order to consistently
elect a good winner. If you don't have polling and thus don't know where
to put the cutoff (between approve and not-approve), you'll face the
Burr dilemma: If you prefer A > B > C, if you "approve" both A and B,
you might get B instead of A, but if you "approve" only A, you might get C!
Thus the kind of Approval that homes in on a good winner employs
feedback. The method is no longer Approval alone, but Approval plus
polling. That /can/ work (people approve {Nader, Gore} if Nader has
fewer votes than Gore, so that Bush doesn't win from the split, but only
approve either Nader or Gore if both are large), but why should we need
to be burdened with the feedback?
Some, like Abd, argue that we always reason based on others' positions
to know how much we can demand, and so that this is a feature rather
than a bug. That doesn't quite sound right to me. In any event, if you
want Approval + bargaining (which the feedback resolves to), make that
claim. Approval alone, without feedback, will be subject to the flaws
mentioned earlier, however.
Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval andrange voting? (long)
On Tue, Nov 10, 2009 at 8:18 AM, robert bristow-johnson wrote: > i will say this: even though it is prohibited in the present IRV that > Burlington VT has, there is no reason that ties should not be allowed in any > ranked ballot. It is unclear how this should work with IRV. My personal preference is that both votes would count at full strength. The other possibility is that they are divided equally between all remaining candidates. In both cases, the count is more difficult. > is that putting it in an accessible context? so then with Approval voting, > for sure this grandma marks "X" by her grandson's name. but does she or > doesn't she Approve her good ol' incumbent? Approval doesn't let you mark > it "Approve except in the race with my top choice." However, if you know who the top-2 are, then this isn't a major problem. The point with approval is that it tends to converge to a condorcet winner, or a candidate who is almost as good. It might even be better at finding honest condorcet winners than an actual condorcet method, assuming that the voters vote tactically in both cases. > i mean isn't that the essential flaw? e.g. the flaw with the Electoral > College is that sometimes it elects the wrong candidate. it does pretty > good when it selects the same winner as the popular vote, but when it > disagrees with the popular vote it *never* creates more legitimacy or > confidence in the election results. so then why have it? what good is it? It would have probably been better if they set it up so the college actually meets, but then add a requirement that the majority of the electors must agree. If combined with PR at the state level when electing electors, then a candidate who has the support of the majority of the population should end up winnng. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval andrange voting? (long)
On Nov 10, 2009, at 6:48 AM, Matthew Welland wrote: Thanks all for the discussion and pointers. I still can't concretely conclude anything yet but here are some rambling and random thoughts based on what was said and my prior experiences. Plurality Leads to two lowest common denominator parties which are not accountable to the voters. This conclusion supported by real world observation. Use of single winner districts has this tendency in general. The other single winner methods below give some more space to third parties but if you want to get rid of favouring the major parties and get proportional representation of all the parties/interest groups then some proportional multi winner methods method could be used. Feels right to the non-critical mind, "one man, one vote" Very fast at the polls Approval Encourages participation of minor parties and thus should keep the big guys paying attention to a wider base. Almost zero marginal implementation cost. Hanging chads count just fine :) Understandable by anyone but feels wrong at first "not fair, you get more than one vote". Apparently has a terrible flaw but no one seems to be able to articulate it in layman terms. No real world experience available to illustrate the problem. Here is where I need to learn more. Data provided to date is unconvincing to me. Here's one example. We have left and right wings with approximately 50%-50% support. Left wing has two candidates (L1, L2). Most right wing voters approve only the right wing candidate (R). Some left wing candidates approve both leftist candidates but some approve only one of them. Right wing candidate wins. In order to avoid this problem left wing might recommend all its supporters to approve both left wing candidates. If they do so left wing will not have the above mentioned problem of vote splitting but on the other hand L1 and L2 will get the same number of votes since nobody can indicate if L1 is better than L2 or the other way around. Choice between L1 and L2 is quite random since the decision will be left to those left wing voters who don't follow the recommended strategy and to those right wing voters who approve also one of the left wing candidates. In this example the problem thus is that voters can not express at the same time both that left/right wing is better and that one of the candidates of that wing is better than some others of them. This problem may lead to interest within the left wing to nominate only one candidate (=no spoilers, no leftist third parties) and we might be close to the plurality related problems again. Approval may work in this case quite well as long as the third party is small and all its voters understand that they should approve also one of the major parties (left), but when the support of that third candidate grows things become more complicated. Does not meet the desire of some to be able to differentiate between "I like", "I like a lot" etc. (note: this seems like perfectionism to me. Large numbers of voters and opinions all over the bell curve should make individual expression at the greater level of granularity irrelevant.) Out of the discussed methods Range is the only one that can express "like"/"like a lot". But it has its own problems (partly due to this property). The example above tries to demonstrate that while large number of sincere Approval votes might statistically lead to a good result there is the risk that the votes will be not as well in balance (for strategy and candidate positioning related reasons). I think it is a general assumption that in Approval voters would not vote sincerely in th sense that they would approve those candidates that they consider "approvable" but they would follow strategy "approve part of the leaders (likely winners) and candidates that you prefer to them". Very fast at the polls. Pick yer favorites and head home for beer and telly. Range Can break the vicious cycle of plurality I didn't understand this. (If this is about the two party dominance I commented already above.) Not voting for someone at all can have a strong influence on election outcome. This is very non-intuitive and would take some getting used to. Allows for nuanced voting. This is the benefit of Range. The related problem is that while this works well in non-competitive elections (e.g. polls, olympics with neutral judges) in competitive ones (e.g. political elections) voters have an incentive to exaggerate. This may lead to Approval-like behaviour where most voters give min and max points to most candidates. In that case Range would be very much like Approval.) Pain in the ass at the polls (relatively speaking). You can't safely disregard the candidates you don't care about so you *have* to assign everyone a ranking, possibly addressable by defaulting to zero for all candidates? This is considered a feature and I a
Re: [EM] NESD and NESD* properties of a single-winner voting method
Dear Warren, I don't seem to understand the definition: > A single-winner voting system "fails the NESD property" if, when every > honest voter > changes their vote to rank A top and B bottom (or B top and A bottom; > depends on the voter which way she goes), leaving it otherwise > unaltered, that always (except in very rare "exact tie" situations) > causes A or B to win. So, when all voters vote strategic (i.e. no voter is honest) and all leave their ballots unchanged, then by definition "every honest voter changes their vote to rank A top and B bottom" but of course no system changes the result since no ballot is changed. Hence no system fails NESD. What is the misunderstanding here? Yours, Jobst Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Anyone got a good analysis on limitations of approval andrange voting? (long)
On Nov 9, 2009, at 11:48 PM, Matthew Welland wrote: Approval Does not meet the desire of some to be able to differentiate between "I like", "I like a lot" etc. (note: this seems like perfectionism to me. Large numbers of voters and opinions all over the bell curve should make individual expression at the greater level of granularity irrelevant.) we should be able to express our preferences. Approval reduces our metric of preference to a 1-bit number, a dichotomy. i would like to have more bits in that number. Suite of complicated systems that strive to reach "Condorcet" ideals. No regular bloke would ever trust 'em because you can't explain how they work in one or two sentences. Round Robin tournament, Ranked Ballot: The contestant who wins in a single match is the candidate who is preferred over the other in more ballots. The candidate who is elected to office is the contestant who loses to no one in the round robin tournament. that's two sentences and two labels. Technically superior to other systems. Not clear what problem with approval they would solve. Unless you are a perfectionist and insist that individuals express nuances of opinion... like which candidate they like better than the other candidate? It was very tedious voting in any of the ranking systems. it's tedious to decide who you like better? who you would prefer if any two candidates are presented? i will say this: even though it is prohibited in the present IRV that Burlington VT has, there is no reason that ties should not be allowed in any ranked ballot. but i would agree it would be tedious to allocate preference points in Range. So, to re-frame my question. What is the fatal flaw with approval? it's essentially like Plurality except you get to mark "X" on more than one candidate (like you do in multi-seat races). i don't like it for multi-seat (in the state senate for the county i am in, all of our senators are elected from the county at large and there are 6 for my county) i always think i'm hurting a candidate i actively support by voting for another candidate from the same party that i approve of. so then i mark "X" on only one candidate and, if enough people vote tactically like that, the election works like Plurality. we want an improvement to Plurality because we might like a three or four party system (or 3 parties and viable independents). we want to not have to consider the likelihood of wasting our vote by deciding who to Approve of. we know we approve of the candidate we support, but it is a tactical decision to decide if you approve of a candidate you would normally approve of but is not the candidate that you have actively supported. like what if you're a little old lady and you like and support you representative legislator for re-election. and you support him over any likely candidate from the other party, and it might be close so you wanna feel like you helped him. but your grandson that you cherish and are proud is running as an independent. in fact you gave money to your grandson's campaign. you support your grandson. you don't know if he'll win or not, but you do not want to harm his chances. you also don't want your good ol' incumbent you've always supported. you want to make sure he doesn't lose to the other major party candidate. but you wouldn't mind harming his chances if the race ended up between him and your grandson. is that putting it in an accessible context? so then with Approval voting, for sure this grandma marks "X" by her grandson's name. but does she or doesn't she Approve her good ol' incumbent? Approval doesn't let you mark it "Approve except in the race with my top choice." I'm not interested in subtle flaws that result in imperfect results. I'm interested in flaws that result in big problems such as those we see with plurality and IRV. how 'bout electing the wrong candidate? i mean isn't that the essential flaw? e.g. the flaw with the Electoral College is that sometimes it elects the wrong candidate. it does pretty good when it selects the same winner as the popular vote, but when it disagrees with the popular vote it *never* creates more legitimacy or confidence in the election results. so then why have it? what good is it? it's either ineffective in "filtering" the popular vote or, when it *is* effective it makes matters worse. such a useful device! with Condorcet you elect the candidate that, from the set of voters who have an opinion, is preferred by a majority of that set over any other candidate that you pick. any winner of an election system that elects a candidate who is not the Condercet winner, has elected someone whom was rejected by the voting majority in favor of the Condorcet winner who wasn't elected. how is that congruent to the principle of democracy? do we have elections and explicitly give it t
