[EM] MMPO revisited

[fsimmons at pcc.edu]

MMPO minimizes the maximum pairwise opposition, so in some sense tries to minimize the  total 
disappointment that results from the MMPO winner being elected instead of some other candidate.

If strict rankings are not required (so that favorite and compromise can be ranked equal first), then 
MMPO satisfies the FBC; no strategic incentive to betray favorite.  This is a feature worth hanging onto.  
Can MMPO be improved while retaining the FBC?

It seems to me that if we use Cardinal Ratings or Range style ballots, we can refine our measure of 
disappointment as follows:

According to a given range ballot, if A is elected instead of B there is no relative disappointment if A is 
rated higher than B, but if B is rated higher than A, the ballot disappointment is evidently the difference in 
their ratings

        r(B)-r(A). 

Sum this relative disappointment over all ballots to get the total disappointment of seeing A elected 
instead of B.

Suppose then that we use Range style ballots and elect the candidate that minimizes the max  total 
disappointment.  Call it MMTD for  MinMaxTotalDisappointment.

Like MMPO  the method MMTD satisfies the FBC.  It is obviously monotone because raising A relative 
to B reduces the ballot disappointment of A being elected instead of B, without decreasing any other 
relative disappointments.

Is it clone free?  Marginally.  By that I mean in the same sense that Range is clone free; if we assume 
that all members of a clone set are rated equally.  If they are rated differently, then the potential violation 
of clone independence is proportional to the discrepency in their ratings.  But then the further apart their 
ratings, the further apart their distance in issue space, and the weaker their claim of being true clones.  

Note that mere ranked ballots do not have the ability to distinguish "fake clones" from true ones in this 
way, because in that setting there is no "degree of cloneness;"  being ranked solidly relative to the other 
candidates is the whole story.

It seems to me that the MMTD winner A has a strong direct claim as best candidate, because if some 
other candidate C wins instead of  A, the total disappointment for C winning instead of A will be larger 
than the disappointment of A winning instead of C. 

In general no matter who wins, there will be disappointed voters.  Why not minimize the total 
disappointment?

Forest