I doubt it's monotonic, though it's probably not a practical problem. That is, it would probably be totally impractical to try to use the nonmonotonicity for anything strategic, and it wouldn't even lead to Yee diagram ugliness.
2011/7/13 <[email protected]> > Here's a simpler version that is basically the same: > > Make use of cardinal ratings so that the rating of candidate X on ballot b > is given by b(X). > > Define the closeness of candidate X to candidate Y as the dot product > > Sum b(X)*b(Y) > > where the sum is taken over all b in the set beta of ballots. > > While there remain two or more candidates, eliminate the pairwise loser of > the two that are least close > to each other. > > > > ----- Original Message ----- > From: Kristofer Munsterhjelm > Date: Wednesday, July 13, 2011 2:35 pm > Subject: Re: [EM] A distance based method > To: [email protected] > Cc: [email protected] > > > [email protected] wrote: > > > Trying to build a metric from a set of ranked ballots is > > fraught with > > > difficulties, and your outline of a procedure for doing it is > > > interesting to me. > > > > > > The simplest, least sophisticated idea I have so far that > > seems to > > > have some use is to define the distance between two candidates > > X and > > > Y to be the number of ballots on which at least one of the two > > is > > > truncated. > > > > I'm not sure if that really works. It could give a rough > > distance > > between zones of acceptable and unacceptable candidates, but > > beyond that > > it gets less reliable. To take a Norwegian example: we have two > > broad > > coalitions: one that's left-of-center and one that's right-of- > > center. > > Say I prefer the left-of-center coalition. I would still rank > > the > > right-of-center coalition's individual parties because "if I > > have to get > > one of them, I could at least try to pull them as close as > > possible to > > my view". > > > > Popularity could also be a factor. In a Bush-Gore-Nader setting, > > voters > > might rank Bush, Gore, and Nader, but skip Browne, Hagelin, and > > Phillips. > > (Truncation would also pose a problem to the inference idea I > > gave in my > > earlier post. In general, noise or variety in the amount of > > information > > provided, in any manner, would. But it makes sense to consider > > perfect > > situations before going to imperfect ones.) > > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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