[EM] A distance based method (monotone version)

[fsimmons at pcc.edu]

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?