Re: [EM] Wikimedia's Board of Trustees elections, 2011
Hallo, Wikimedia has now published details of the latest Board of Trustees elections: http://meta.wikimedia.org/wiki/Board_elections/2011/Results/en There was a circular tie for positions 7 to 9. Cain beat Richardson 861:818. Richardson beat Lorente 838:832. Lorente beat Cain 789:784. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Eric Maskin promotes the Black method
Hallo, Eric Maskin, a Nobel laureate, is currently very active in promoting the Black method. The Black method says: If there is a Condorcet winner, then the Condorcet winner should win; if there is no Condorcet winner, then the Borda winner should win. See e.g.: 1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268 8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww Maskin argues as follows: If election method X is the best possible election method in domain X and if election method Y is the best possible election method in domain Y and if domain X and domain Y are disjoint and if domain X and domain Y together cover all possible situations, then the best possible election method is to use election method X in domain X and election method Y in domain Y. Maskin argues: domain X = situations with a Condorcet winner; election method X = any Condorcet method; domain Y = situations without a Condorcet winner; election method Y = Borda method. *** That method, that uses election method X in domain X and election method Y in domain Y, will be called election method Z. *** Maskin's argumentation doesn't work because of the following reason: Whether an election method is good or bad depends on which criteria it satisfies. Most criteria say how the result should change when the profile changes. Now it can happen that the original profile and the new profile are in different domains. This means that, to satisfy some criterion, election method X for domain X and election method Y for domain Y must not be chosen independent from each other. Example: The participation criterion says that adding some ballots, that rank candidate A above candidate B, must not change the winner from candidate A to candidate B. Election method X satisfies the participation criterion in domain X. Reason: If candidate A was the winner in the original profile and if the original profile was in domain X, then this means that candidate A was the Condorcet winner and, therefore, that candidate A pairwise beat candidate B. If candidate B is the winner in the new profile and if the new profile is in domain X, then this means that candidate B is the Condorcet winner and, therefore, that candidate B pairwise beats candidate A. If candidate A pairwise beat candidate B in the original profile and if candidate B pairwise beats candidate A in the new profile, then this means that the added ballots rank candidate B above candidate A. Election method Y satisfies the participation criterion in domain Y, because the Borda method satisfies the participation criterion in general. However, election method Z doesn't satisfy the participation criterion since the Condorcet criterion and the participation criterion are incompatible. In short: Even if election method X satisfies criterion A in domain X and election method Y satisfies criterion A in domain Y, it doesn't mean that election method Z satisfies criterion A. Therefore, Maskin's argumentation doesn't work. *** I also question the claim that the Borda method is the best possible election method in situations without a Condorcet winner. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Eric Maskin promotes the Black method
Markus Schulze wrote: Hallo, Eric Maskin, a Nobel laureate, is currently very active in promoting the Black method. The Black method says: If there is a Condorcet winner, then the Condorcet winner should win; if there is no Condorcet winner, then the Borda winner should win. (...) Maskin's argumentation doesn't work because of the following reason: Whether an election method is good or bad depends on which criteria it satisfies. Most criteria say how the result should change when the profile changes. Now it can happen that the original profile and the new profile are in different domains. This means that, to satisfy some criterion, election method X for domain X and election method Y for domain Y must not be chosen independent from each other. I find it strange for a Nobel laureate (and within mechanism design at that!) to not notice this. I've mentioned my concept of discontinuity before, and it seems quite obvious that if you stitch together two methods, you can't just look at how one method behaves and how the other does, but also the boundary between the two. To my knowledge the Participation and LNH incompatibility proofs against Condorcet work this way: they show that no matter how you smooth the transition between the Condorcet domain and the non-Condorcet domain, there will be sudden transitions (discontinuities) and you can't line them all up at the same time. Moreover, I agree with you that Borda doesn't seem to be very good. Well, it works when there's no strategy (and it gets respectable regret in such cases), but strategy is very obvious and can backfire horribly (as by Warren's NEC example where the mediocre candidates win because of massive burial). The burial strategy may be obvious enough that voters would engage in it even if they thought there would be a CW. They would think that perhaps there won't be a CW and in that case I should maximize the effect of my vote, similar to how FPC could encourage compromising in a Nader/Bush/Gore scenario. Finally, if one accepts that the Condorcet criterion makes sense, and to comply with it is best when there is a CW, why not expand? Why not limit oneself to the Smith set, or to uncovered candidates? The decision to be Condorcet compliant but to go no further in the Condorcet direction seems rather arbitrary. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Eric Maskin promotes the Black method
Dear all, Why not write an open letter to him (i.e. publish the letter on this list) and invite him to further discuss on this list? I found Maskin's email: mas...@ias.edu in his CV, which is online. If hybrid methods is the way to go, then the forthcoming paper in Voting matters which Kristofer linked to seems to be better than his Condorcet-Borda: http://www.votingmatters.org.uk/FORTHCOMING/I29P1f.pdf Peter On Tue, Jun 21, 2011 at 1:56 PM, Markus Schulze markus.schu...@alumni.tu-berlin.de wrote: Hallo, Eric Maskin, a Nobel laureate, is currently very active in promoting the Black method. The Black method says: If there is a Condorcet winner, then the Condorcet winner should win; if there is no Condorcet winner, then the Borda winner should win. See e.g.: 1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268 8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww Maskin argues as follows: If election method X is the best possible election method in domain X and if election method Y is the best possible election method in domain Y and if domain X and domain Y are disjoint and if domain X and domain Y together cover all possible situations, then the best possible election method is to use election method X in domain X and election method Y in domain Y. Maskin argues: domain X = situations with a Condorcet winner; election method X = any Condorcet method; domain Y = situations without a Condorcet winner; election method Y = Borda method. *** That method, that uses election method X in domain X and election method Y in domain Y, will be called election method Z. *** Maskin's argumentation doesn't work because of the following reason: Whether an election method is good or bad depends on which criteria it satisfies. Most criteria say how the result should change when the profile changes. Now it can happen that the original profile and the new profile are in different domains. This means that, to satisfy some criterion, election method X for domain X and election method Y for domain Y must not be chosen independent from each other. Example: The participation criterion says that adding some ballots, that rank candidate A above candidate B, must not change the winner from candidate A to candidate B. Election method X satisfies the participation criterion in domain X. Reason: If candidate A was the winner in the original profile and if the original profile was in domain X, then this means that candidate A was the Condorcet winner and, therefore, that candidate A pairwise beat candidate B. If candidate B is the winner in the new profile and if the new profile is in domain X, then this means that candidate B is the Condorcet winner and, therefore, that candidate B pairwise beats candidate A. If candidate A pairwise beat candidate B in the original profile and if candidate B pairwise beats candidate A in the new profile, then this means that the added ballots rank candidate B above candidate A. Election method Y satisfies the participation criterion in domain Y, because the Borda method satisfies the participation criterion in general. However, election method Z doesn't satisfy the participation criterion since the Condorcet criterion and the participation criterion are incompatible. In short: Even if election method X satisfies criterion A in domain X and election method Y satisfies criterion A in domain Y, it doesn't mean that election method Z satisfies criterion A. Therefore, Maskin's argumentation doesn't work. *** I also question the claim that the Borda method is the best possible election method in situations without a Condorcet winner. Markus Schulze Election-Methods mailing list - see http://electorama.com/em for list info Election-Methods mailing list - see http://electorama.com/em for list info
[EM] Something better than wv for Schulze's CSSD
I am more convinced than ever that the best way to measure defeat strength in Beatpath (aka CSSD) is by giving the covering relation the highest priority, and where neither alternative covers the other, falling back on winning votes. This is a natural way to extend the covering relation (which is a partial order) to a total ordering of the candidates. So if A covers B, then that beatpath with one link is stronger than any beatpath that B can have to A. If neither A nor B covers the other, then all beatpaths in both directions have links (defeats) that are not coverings (because the covering relation is transitive). The strength of a beatpath that has at least one link that is not part of the covering relation is the wv strength of the weakest such link. If we say that AB whenever the strongest (in the above sense) beatpath from A to B is stronger than any beatpath from B to A, then the relation is a total order barring exact ties at weakest links. If range style ballots are used to infer the voter rankings, then these ties can be resolved without use of randomness. Among the tied candidates give preference to the one with positive ratings on the greatest number of ballots. If the tie is still not resolved, break it by giving preference to the still tied candidate rated above one on the greatest number of ballots. If still tied, give preference to the still tied candidate rated above two on the greatest number of ballots, etc. If we use the above method of defining defeat strength, we can still use the CSSD algorithm to find the Beatpath winner. The method retains its clone free property, and its compliance with the Monotonicity Criterion. Beyond that it always elects an uncovered alternative. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Eric Maskin promotes the Black method
On Jun 21, 2011, at 7:56 AM, Markus Schulze wrote: Hallo, Eric Maskin, a Nobel laureate, is currently very active in promoting the Black method. i have to confess, even though i had heard of ranked-choice voting before and had myself thought that what would later to be learned is called Condorcet compliant was the only logical and consistent (with a simple majority binary vote in all binary cases) manner to decide it. and i thought of the possible problem that there was no single candidate who wins every pair they're in, didn't know what to call it, and didn't even know if there were any theorems that spoke to it, and decided not to worry about it. anyway, because i'm a real neophyte to this, it wasn't until sometime last decade that i read anything about it until i read a Scientific American article of his titled The fairest vote of all that promoted Condorcet, but didn't really call it that. Maskin labeled the method true majority rule and only obliquely raised the issue that a cycle could happen and mentioned Condorcet in that context. soon after i learned the terms from the Wikipedia articles and at about the same time, we voted in IRV by about 65% (which was repealed in 2010 in a dramatic but really stupid slugfest between the one true faith One person, one vote crowd and those who denied anything went wrong in the 2009 election). anyway, especially after reviewing his bio again, i can't help by admire the guy and it was an article of his that first got me thinking analytically about the voting systems issue. but i wonder if he was using terminology that was more neology, even pre-neology. i think he was trying to coin a term that would end up getting attached to his name. and we've all been groping for a name for this primary voting criteria that is not this non-American, Frenchie, probably sorta pinko- socialist secular humanist intellectual (did i mention *not* American?) whose heresy is leading us away from the One True Faith of the Single Affirmative Vote. we have sects in the One True Faith, some of us believe in the sanctity of the Two Party System: if yer ain't fer us, you agin' us. and pass da ammunition, Ma. i don't have a better idea than true majority rule. but there must be a better one than that. Warren, i remember you like beats-all winner for the CW. i wonder if the beats-all method is a good label. The Black method says: If there is a Condorcet winner, then the Condorcet winner should win; if there is no Condorcet winner, then the Borda winner should win. i hadn't heard of the Black method before, but just reading this shows pretty superficially a problem. above is one way to say something... See e.g.: 1 Sep 2009: http://research.microsoft.com/apps/video/default.aspx?id=143268 8 Apr 2011: http://www.youtube.com/watch?v=Bx_lt06W9Ww Maskin argues as follows: If election method X is the best possible election method in domain X and if election method Y is the best possible election method in domain Y and if domain X and domain Y are disjoint and if domain X and domain Y together cover all possible situations, then the best possible election method is to use election method X in domain X and election method Y in domain Y. Maskin argues: domain X = situations with a Condorcet winner; election method X = any Condorcet method; domain Y = situations without a Condorcet winner; election method Y = Borda method. ... and this is another way to say the same thing. so, right away, Maskin is just restating an assertion as some sort of argument supportive of the assertion, but it is nothing new. just a re- assertion. (is that what is begging the question is?) at the core, let's assume that we are already disciples of Condorcet, we all agree that method X is best for domain X, he doesn't say squat about why method Y is preferred in domain Y. if we're nowhere near to a conclusion that Borda is good for anything (he might have been a good general, i dunno), then how do we conclude that it is preferable to everything else when there is no CW? sorry, i haven't even got past this block. Maskin's argumentation doesn't work because of the following reason: Whether an election method is good or bad depends on which criteria it satisfies. Most criteria say how the result should change when the profile changes. Now it can happen that the original profile and the new profile are in different domains. This means that, to satisfy some criterion, election method X for domain X and election method Y for domain Y must not be chosen independent from each other. but, this is the fundamental argument of those who claim that it is natural for an election to be spoiled, to be dependent upon irrelevant alternatives. isn't that what the fundamental issue is about for why Condorcet (assuming a CW exists) is consistent with any simple- majority, two-candidate
