Hi Jameson, --- En date de : Jeu 21.7.11, Jameson Quinn <[email protected]> a écrit : >>By "meaningful" you don't mean "sincere" or something do you? > >Well... sorta. More like "anchored by sincerity". The point is that >with real voters, if strategic pressure isn't too strong, the median >will stay at some predictable place, which then can be used for >others' strategy. With simulated voters, the smallest strategic >pressure, or even a random walk, will eventually push the median to >max or min rating, and then the method loses its power of >discrimination. > >So I'm not hoping that everyone will be "sincere", I'm just positing >that "sincere" should have some meaning which voters can fall back >on if there isn't any particular strategic reason not to. This is >similar to Balinski and Laraki's insistence on "common terminology >of judgment", which they spend several chapters of their book >discussing.
Oh, I see. I guess I'm not sure how common this kind of situation would be in a public election. For some candidates I will always want to vote in a strategic fashion, and it feels odd to me to consider voting other candidates in a sincere fashion right on the same ballot. [begin quote] Let me be define the terms. If the pair with the greatest approval coverage is A and B, then "approval-decisive votes for A" D(A,X) at threshold X means the absolute number of ballots with A above X and B below X. The "mutual approval" M(X) is the number of ballots which approve both A and B; and the "mutual disapproval" U(X) is the ballots which disapprove both. Possible cutoff metrics to maximize: D(A,X) + D(B,X) : (what I suggested) On second thought, this could elect the guy who most thoroughly beats Hitler. D(A,X) * D(B,X) : Avoids the problem above, but too much of a focus on "contested" results, whether or not these are majority results min(D(A,X), D(B,X)) : like the previous, but worse -max(M(X), U(X)): this looks good to me. Unlike the metric I first suggested, this does target some form of "median" for the cutoff. -(M(X) * U(X)): Similar to the previous So, I guess I'm saying, instead of maximizing the approval-decisive votes, minimize the max of (the mutual approvals or the mutual disapprovals). Or perhaps their product. [end quote] Just to be clear, you're saying one selects the cutoff (which will be uniform across all ballots) such that it maximizes/minimizes a certain score for any pair of candidates. That's what makes sense to me as I'm thinking about this. But let me know if it's wrong. Thanks. Kevin Venzke ---- Election-Methods mailing list - see http://electorama.com/em for list info
