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
