[EM] A distance based method

[fsimmons at pcc.edu]

First find a clone consistent way of defining distance between candidates.

Then while two or more candidates remain
  of the two with the greatest distance from each other
  eliminate the one with the greatest pairwise defeat
EndWhile.

Various variants are possble.  For example, you could count defeats only from the remaining 
candidates.  Also there are various possible measures of defeat strength.  In that regard, if you say that 
any defeat by covering is stronger than every non-covering defeat, then the method will always elect a 
covered candidate.

To get a distance estimate in a large election you could just ask each voter to list the pair of candidates 
that seem the most different on the issue or combination of issues of most concern (to that voter).  The 
pair submitted by the greatest number of voters would be the first pair considered, etc.

What potential for manipulation does this direct approach introduce?

Perhaps voters would try to pit their favorites' rivals against each other.  Would that be insincere?  Not if 
they consider their favorite to have a reasonable middle of the road position, while viewing the rivals as 
being at opposite unreasonable extremes.

What indirect measure of distance could be used?

If we count the number of ballots on which candidates X and Y are ranked at opposite extremes (top 
rank for one versus unranked for the other), the monotonicity of the method would probably be 
destroyed.  Is there a more subtle way of inferring the distance that wouldn't destroy the monotonicity?