See below for the context. I thought aloud a few years ago that one way to select a "winning ranked ballot" would be to find the ballot that is "most like" the consensus ballot. Order the candidates by their Bucklin rank and ballots by the Kendall tau "distance" that each ballot is from the Bucklin rank. The ballot with the least tau distance from the medians is then used to decide the election.
(Based upon a science fiction short-story from the 1950s, but reasonable from a mathematical perspective.) -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Raph Frank Sent: Saturday, January 03, 2009 6:13 PM To: Kristofer Munsterhjelm Cc: Election Methods Mailing List Subject: Re: [EM] Feature extraction and criteria for multiwinner elections On Sat, Jan 3, 2009 at 1:40 PM, Kristofer Munsterhjelm <[email protected]> wrote: > A (seemingly) reasonable generalization of the Euclidean distance Voronoi > would be this: For each point, find the two candidate points so that the sum > of the distances to those two points are minimized. Color p according to the > composite color of the k closest candidates (for a (k,n) election). But > doesn't that correspond to the election method where you elect the CW, then > remove him and elect the next CW and continue like that until done? That > method is not PR. One option would be for each possible set of N winners - find the average distance from each voter to the closest winner The 'best' winning set is the one that minimises this average distance. This means that the size of the Gaussian would matter. If all the voters were concentrated at a single point, then the winner would just be the double CW like you said. However, if there is a large spacing between the voters, then it the effect would be to elect candidates closer to the edges. > 46: Left > Center > Right > 46: Right > Center > Left > 8: Center > Left > Right > > which should elect Center in a single-winner election, but Left and Right in > a multiwinner one? Yes, I think this is perfectly reasonable. Centre is a compromise between all the voters. However, if there are 2 seats, then each faction should be allowed to pick its own winner. Left + Right means that 92% of the voters get their top choice elected. Which is better than Centre + Right or Centre + Left. ---- Election-Methods mailing list - see http://electorama.com/em for list info ---- Election-Methods mailing list - see http://electorama.com/em for list info
