[EM] MinMax variant

[Forest Simmons]

Has anybody ever proposed minimizing the maximum opposition rather than
minimizing the maximum defeat?

I know that theoretically this could elect the Condorcet Loser, but it
seems very unlikely that it would do so.

It seems to me that if equality were allowed in the rankings, then this
method would satisfy the FBC, since ranking Favorite equal with Compromise
wouldn't increase opposition against Compromise.

Venzke Kevin has recently suggested a version of this method adapted to
approval ballots.

I wonder how well it would work with CR ballots having resolution greater
than two.

You would start with the pairwise matrix whose (i,j) entry is the number
of ballots expressing a preference for candidate i over candidate j.

Then you would find the maximum entry in each column.

Then the minimum of these numbers corresponds to the candidate whose
maximum opposition is minimum.

This method differs from the usual MinMax in that it considers all
opposition, not just opposition resulting in defeat.

Forest