[EM] A distance based method (monotone version)

[fsimmons at pcc.edu]

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?