Re: [EM] Better Approval-voting option? Could ABucklin fail FBC?
Hi Mike, De : MIKE OSSIPOFF >À : election-meth...@electorama.com >Envoyé le : Jeudi 1 mars 2012 15h55 >Objet : [EM] Better Approval-voting option? Could ABucklin fail FBC? > > >But could this happen?: > >If you rank your favorite, F, in 1st place, s/he gets a majority, even though >s/he doesn't win, because someone else has a higher >majority. > >A number of people rank F, and, if you help F get a majority, then they won't >give a vote to their next choice. > >That's regrettable, because their next choice could win with those votes, >while F can't win. And when their next choice doesn't win, >someone worse than s/he (as judged by you) wins. > >You got a worse result because you didn't favorite-bury. > >So maybe, even if that scenario is merely possible, I shouldn't propose >Stepwise-to-Majority unless it turns out that the FBC-failure scenario >can't happen. > >But more worrying is the fact that one could tell that same story about >ABucklin (the ER-Bucklin defined at electowiki). > >Of course a vague verbal scenario like the above might not have an actual >numerical example that can carry it out. There might >be some reason why such an example couldn't work. Still, it's worrying. > >Does anyone know if there's actually a proof that ER-Bucklin meets FBC? > >Can it be shown that the verbal FBC-Failure scenario described above couldn't >really happen? > >Might ABucklin fail FBC? > I want to help but I'm not sure I understand the failure scenario you described. With three candidates ER-Bucklin(whole) gives the same results as MCA. There can't be much doubt that MCA satisfies FBC. But maybe you have in mind a scenario with more than three candidates? Off the top of my head I would argue that ERBW satisfies FBC because when you raise your favorite to equal-top, this can only delay the reception of votes for candidates that you like less than your top candidates (because it's only on your own ballot that this has an effect). You aren't doing anything to delay acquisition of votes by your top-ranked compromise choice from other voters. Any thoughts? Kevin Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] SODA sometimes FBC-safe
2012/3/1 MIKE OSSIPOFF > Jameson: > > You wrote: > > Actually, with SODA, it does help, because you can know ex ante (by > looking at the predeclared preferences) when you are safe by FBC. That is, > if you prefer A>B, and B prefers A, or A prefers B, or A and B both prefer > a certain viable C, then you are safe. Only if B prefers the most-viable > third candidate C, but A is indifferent between B and C, then you might > consider a favorite-betraying vote for B. And even then, it's only > appropriate if A very nearly, but not quite, is able to win... not exactly > the situation where favorite betrayal is the first thing on your mind. > > This is a specific enough circumstance that favorite-betraying strategy > would never "take off" and become a serious factor in SODA. > > With SODA, you can give that as a solid ex-ante guarantee to most voters, > just not quite all of them. This is unlike the situation in most voting > systems, where you can make no solid guarantees before the vote unless you > can make them to all voters. > > [endquote] > > Ok yes, as you say, that's a very different situation from the ordinary > FBC-failure, because, for most people there is known to be no > favorite-burial need. The favorite-burial problem really > exists when there's uncertainty for everyone, or for a large percentage of > the voters, which isn't the case with SODA. > > Thank you. By the way, I left out one further circumstance in which you are FBC-safe. Using the letters above, you are also safe if C declared a preference for B. If C prefers A or is indifferent between A and B, then you might have to worry (if all the other circumstances listed above also pertain.) Jameson Jameson Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Better Approval-voting option? Could ABucklin fail FBC?
Though the options of voting as in AOCBucklin, MTAOC or MCAOC in an Approval election make some sense, when the election is regarded as that kind of election, with some people (the Approval-ballot voters) rating everyone at top-rank, one can't help noticing that some aspects of those vote-management options, in an Approval election, seem suboptimal for the voter. Two conclusions suggest themselves: 1. Maybe MTA, MCA and ABucklin don't often really improve on Approval. Maybe Approval-style voting is often the best strategy in those methods. 2. Maybe there could be a better vote-management option in an Approval election. Regarding #2, how about Stepwise-to-Majority? I'd previously proposed Middle-When-Needed, and Stepwise-When-Needed. Stepwise-When-Needed could be called Stepwise-to-Win. The rankings, as in Bucklin, keep simultaneously giving a vote to their next choice, stepwise, by stages, as in ABucklin, each ballot continuing to do so as long as no candidate it's already given to is the current winner. I acknowledged, at that time, that it would often turn out to be no different from an Approval count of all the ranked candidates. Then I noticed that the those 2 methods probably fail FBC. I wondered if there's something somewhat similar that meets FBC. Maybe, judging candidates by an arbitrary number like majority would avoid the problem, as opposed to judging by whether one of your higher ranked candidates is winning. Hence, Stepwise-to-Majority. During the Buckliln-like vote-giving stages, each ballot keeps giving to its next choice till someone it has given to has a majority. But could this happen?: If you rank your favorite, F, in 1st place, s/he gets a majority, even though s/he doesn't win, because someone else has a higher majority. A number of people rank F, and, if you help F get a majority, then they won't give a vote to their next choice. That's regrettable, because their next choice could win with those votes, while F can't win. And when their next choice doesn't win, someone worse than s/he (as judged by you) wins. You got a worse result because you didn't favorite-bury. So maybe, even if that scenario is merely possible, I shouldn't propose Stepwise-to-Majority unless it turns out that the FBC-failure scenario can't happen. But more worrying is the fact that one could tell that same story about ABucklin (the ER-Bucklin defined at electowiki). Of course a vague verbal scenario like the above might not have an actual numerical example that can carry it out. There might be some reason why such an example couldn't work. Still, it's worrying. Does anyone know if there's actually a proof that ER-Bucklin meets FBC? Can it be shown that the verbal FBC-Failure scenario described above couldn't really happen? Might ABucklin fail FBC? Mike Ossipoff Election-Methods mailing list - see http://electorama.com/em for list info
[EM] SODA sometimes FBC-safe
Jameson: You wrote: Actually, with SODA, it does help, because you can know ex ante (by looking at the predeclared preferences) when you are safe by FBC. That is, if you prefer A>B, and B prefers A, or A prefers B, or A and B both prefer a certain viable C, then you are safe. Only if B prefers the most-viable third candidate C, but A is indifferent between B and C, then you might consider a favorite-betraying vote for B. And even then, it's only appropriate if A very nearly, but not quite, is able to win... not exactly the situation where favorite betrayal is the first thing on your mind. This is a specific enough circumstance that favorite-betraying strategy would never "take off" and become a serious factor in SODA. With SODA, you can give that as a solid ex-ante guarantee to most voters, just not quite all of them. This is unlike the situation in most voting systems, where you can make no solid guarantees before the vote unless you can make them to all voters. [endquote] Ok yes, as you say, that's a very different situation from the ordinary FBC-failure, because, for most people there is known to be no favorite-burial need. The favorite-burial problem really exists when there's uncertainty for everyone, or for a large percentage of the voters, which isn't the case with SODA. Mike Ossipoff Election-Methods mailing list - see http://electorama.com/em for list info
[EM] "Tablebases" and inverting proportionality models
I think I have found a way to help the design of multiwinner methods. As you may know, I've been using a proportionality measure to find the degree to which multiwinner methods give proportional representation, and along with Bayesian regret, to define the current Pareto front of BR versus disproportionality for multiwinner methods that we know of. Some of these tradeoff results are given at http://munsterhjelm.no/km/elections/multiwinner_tradeoffs/ . Some time ago, I was playing with numbers, trying to figure out how many distinct ranked ballot sets exist for a given number of voters and candidates. Because we would expect any reasonable voting method to obey neutrality and symmetry (invariance under permutations of voter and candidate orders), the number of distinct ranked ballot sets turn out to be much smaller than I expected. If we consider ranked ballots without equal rank or truncation, then the number is (n + k - 1) choose k, where k is the number of voters - 1, and n is the factorial of the number of candidates. For 3 candidates, we have, for instance: num voters = 10, num ballot sets = 2002(11 bits) num voters = 25, num ballot sets = 118 755 (17 bits) num voters = 50, num ballot sets = 3 162 510 (22 bits) num voters = 100, num ballot sets = 91 962 520 (27 bits) So with a small number of voters, we could store the mean disproportionality and regret for all possible ballot sets, and if each set has a sufficient number of samples, we could look up any given ballot set and simply see how disproportional each outcome is, on average. What does that give us? My proportionality metric works by giving each candidate and voter a certain binary issue profile, where a given voter is either for or against a given issue. Then it constructs ballots that are consistent with this: voters rank candidates with like issue positions ahead of those with dissimilar positions; and the proportionality per issue of the outcome picked by a multiwinner method can be compared in terms of how many of the council members are in favor of issue one (two, n) versus how many of the voters are so. However, that metric starts from issue profiles and generates ballot sets. It can't go in the other direction by itself. Yet with the "tablebase" - a map from ballot sets to sets of performance numbers - we can do so easily. By noting the disproportionality of every outcome for the ballot sets as we encounter those ballot sets, we can build a record of the function so as to invert it afterwards. And how does that help in mechanism design? Usually, for two-of-three elections, the pattern is that one outcome is dominated by the other two (i.e. the other two have both lower regret and disproportionality), and then one outcome is more proportional but has more regret, and the last outcome has less regret but is less proportional also. By looking at these ballot sets and outcomes, we can try to come up with rules that keep the dominated solutions from being picked. Inverting the proportionality metric would also make it possible to determine the Pareto front for all ranked methods within the binary issue model given (and the constraints on number of candidates and voters). A brute-force approach would simply note that each possible decisive method has to give an outcome for all (or most of) the ballot sets, and plot the Pareto front of the performance of every possible outcome combination. But if there are 1000 ballot sets and 3 possible outcomes for each, that's 3^1000, which is clearly infeasible. Dynamic programming can probably make it feasible again. Regarding criteria, the map could be used to find out how much a certain criterion constrains outcomes. That could be done directly as well (without the need for storage), but using a map could give some idea of how passing a criterion limits the Pareto front, too. Finally, one could use the tablebase to make a Yee diagram for an "optimal" method (again, given the constraints and model). Just define an indifference function (how much disproportionality people are willing to accept for lowered majoritarian regret), then when given a certain ballot set by the Yee generator, determine which outcome is best according to the indifference function and respond as if the (unknown) method chose that outcome. It isn't trivial, though: Yee drawing usually involves having hundreds if not thousands of voters. Perhaps one could use some sort of repeated sampling or antialiasing to get a conclusive result even with <100 voters per sample. Election-Methods mailing list - see http://electorama.com/em for list info
