2013/4/3 Forest Simmons <[email protected]> > > > On Wed, Apr 3, 2013 at 12:07 AM, Kristofer Munsterhjelm < > [email protected]> wrote: > >> On 04/03/2013 12:01 AM, Forest Simmons wrote: >> >>> Jobst has suggested that ballots be used to elicit voter's "consensus >>> thresholds" for the various candidates. >>> >>> If your consensus threshold for candidate X is 80 percent, that means >>> that you would be willing to support candidate X if more than 80 percent >>> of the other voters were also willing to support candidate X, but would >>> forbid your vote from counting towards the election of X if the total >>> support for X would end up short of 80 percent. >>> >>> The higher the threshold that you give to X the more reluctant you are >>> to join in a consensus, but as long as your threshold t for X is less >>> than than 100 percent, a sufficiently large consensus (i.e. larger than >>> t percent) would garner your support, as long as it it is the largest >>> consensus that qualifies for your support. >>> >>> A threshold of zero signifies that you are willing to support X no >>> matter how small the consensus, as long as no larger consensus qualifies >>> for your support. >>> >>> I suggest that we use score ballots on a scale of 0 to 100 with the >>> convention that the score and the threshold for a candidate are related >>> by s+t=100. >>> >>> So given the score ballots, here's how the method is counted: >>> >>> For each candidate X let p(X) be the largest number p between 0 and 100 >>> such that p(X) ballots award a score strictly greater than 100-p to >>> candidate X. >>> >>> The candidate X with the largest value of p(X) wins the election. >>> >> >> I think a similar method has been suggested before. I don't remember what >> it was called, but it had a very distinct name. >> >> It went: for each candidate x, let f(x) be the highest number so that at >> least f(x)% rate the candidate above f(x). >> >> I *think* it went like that, at least. Sorry that I don't remember the >> details! > > > Good memory, that was Andy Jennings' Chiastic method. Graphically these > two methods are based on different diagonals of the same rectangle. >
Different, how? It seems to me they're just the same, but with the numbers reversed. > >> >> If there are two or more candidates that share this maximum value of p, >>> then choose from the tied set the candidate ranked the highest in the >>> following order: >>> >>> Candidate X precedes candidate Y if X is scored above zero on more >>> ballots than Y. If this doesn't break the tie, then X precedes Y if X >>> is scored above one on more ballots than Y. If that still doesn't break >>> the tie, then X precedes Y if X is scored above two on more ballots than >>> Y, etc. >>> >>> In the unlikely event that the tie isn't broken before you get to 100, >>> choose the winner from the remaining tied candidates by random ballot. >>> >> >> I imagine Random Pair would also work. >> >> >> The psychological value of this method is that it appeals to our natural >>> community spirit which includes a willingness to go along with the group >>> consensus when the consensus is strong enough, as long as there is no >>> hope for a better consensus, and as long as it isn't a candidate that we >>> would rate at zero. >>> >> >> That's an interesting point. I don't think that factor has been >> considered much in mechanism design in general. Condorcet, say, is usually >> advocated on the basis that it provides good results and resists enough >> strategy, and then one adds the reasoning "it looks like a tournament, so >> should be familiar" afterwards. >> >> Perhaps there's some value in making methods that appeal to the right >> sentiment, even if one has to trade off "objective" qualities (like BR, >> strategy resistance or criterion compliance) to get there. The trouble is >> that we can't quantify this, nor how much of sentiment-appeal makes up for >> deficiencies elsewhere, at least not without performing costly experiments. > > I'm currently doing such "costly experiments" on Amazon MTurk (with money from Harvard). I'm evaluating Approval, Borda, Condorcet (3-candidate, so the differences between the most common varieties doesn't matter), GMJ, IRV, Plurality, Score, and SODA (with honest-declaring and mutually-rational-assigning AI candidates), with an 18-voter, 3-candidate scenario in factions of 8, 4, and 6 (with utilities for each voter of 0-3, summing to 12, 16, and 11). I'll let the list know as results are available. Jameson
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