2011/7/21 Kevin Venzke <[email protected]> > Hi Jameson, > > --- En date de : Jeu 21.7.11, Jameson Quinn <[email protected]> a > écrit : > >>[begin quote] > >>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. > > What puzzles me is that I don't know how to pick the pair without > knowing the threshold. Yet the reverse seems true also. > > I *think* this is what you do, or can do: > > For each pair, find the best possible score this pair could have by > moving the threshold. (So, for each pair you try every threshold. The > best score ever achieved indicates the winning pair.) >
Yes. Of course you can go the other way around, too: for each threshold, try every pair. > > I did an example on paper. In my example the "M" score was almost > always zero, which makes me doubt the M*U product will work well in > sims. Also, disfavoring a high M score has an obvious favorite > betrayal incentive which (at least in SC) is noticeable. Can you explain further? I don't see how it has any non-semi-honest incentive at all. Perhaps it does have a bullet incentive, though. > Maybe one > could just look at U (like SC does). > But then the threshold is always pushed down. How about maximizing D(A) * (D(A) + D(B))? Or D(A) * (D(A) + D(B) + M), which is the same as D(A) * (V-U)? > In my example the threshold made no difference, as the same pair would > win. So, if I were just picking the pair which can get the best score > one way or another, I would dodge the question of how to break ties > between two thresholds. > > Kevin Venzke > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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