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
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