2011/7/21 Kevin Venzke <[email protected]> > 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. >
Yes, but in many cases, you can be "strategic" without too much distortion. For instance, if you are strategically voting A>B, or A>cutoff, that does not mean that you must push A to the top rank, if there is a predictable cutoff; but if there are no "sincere anchors" for other voters, it probably does. > > [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. > Almost. So that it maximizes / minimizes the score for the pair of candidates selected for the the Single Contest. Although setting it so that it maximizes/minimizes for any pair is also feasible, and might work well. JQ
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