To ensure Plurality compliance, when there is no majority defeat in a pairwise comparison, of the two being compared eliminate the one with the fewest positive ratings.
> The simplest monotone distance based method is this: > > Range ballots are voted and submitted by the voters. > > Initialize candidate variable X as the candidate with the fewest > positive ratings. > > While there remain two or more candidates .. > replace X with the the pairwise winner of > the candidate most distant from X and X itself > (and then eliminate the loser of this pairwise contest) > EndWhile > > Elect the candidate represented by the final value of X. > > This method is obviously monotone, clone free, and less > susceptible to Plurality failure than my previous > version. It has little incentive for compromising, because > Favorite and Compromise are apt to be close > to each other, so they will not be pitted against each other > until the very end if at all. > > This non-compromising feature can be enhanced by (temporarily) > collapsing the top two levels of the > range while computing the distances. This places Favorite and > Compromise at maximum proximity > while still allowing Favorite to be ranked ahead of Compromise > for their pairwise comparison (should they > survive long enough for that to happen). > > Remember that the pairwise proximity of candidates X and Y is > measured by the value > > sum over all ballots b of b(X)*b(Y) , > > where b(X) and b(Y) are the respective ratings for candidtes X > and Y on ballot b. > > With the temporary identification or collapse of the top two > levels this becomes > > sum over all ballots b of min(b(X)*b(Y), h*h) > > where h is the second highest possible rating. > > In cases of ties for max distance from X choose the tied > candidate with the fewest positive ratings. > > In case of ties for fewest positive ratings, choose the tied > candidate with the fewest number of ratings > greater than one, etc. > > This system of tie breakers totally obviates the need for any > further tie breakers, In fact, being still tied > at the end of this system would require that two candidates > receive identical ratings on each and every > ballot. > > According to the examples I have considered the method seems to > be fairly burial resistant, too. > > What do you think? ---- Election-Methods mailing list - see http://electorama.com/em for list info
