[EM] Elimination by MinPO to the MMPO candidate.

[Forest Simmons]

Chris has been keeping me humble ... shooting down my worst nonsense ...
while Kristofer has been busy cleaning up code ... so watch out for an
explosion of progress!

Think of the MMPO candidate C as being located in the midst of the other
candidates in such a way that the smallest neighborhood centered on C that
is large enough to contain the other candidates is as small as possible.

If you extend a line segment from C to another candidate X on the outskirts
of that neighborhood, and then cut that segment with a perpendicular
bisecting plane ... that plane will separate the voters closer to X from
the voters closer to C.

The number of voters closer to X is known as X's Pairwise Opposition to C
in that pairwise contest.

This imaginary schematic suggests that the candidate X with the least PO to
C, would be a good one to eliminate in a single winner method.

Accordingly ... when every candidate suffers at least one pairwise defeat,
we suggest the following elimination procedure:

While more than two candidates remain ... Eliminate the candidate that is
defeated pairwise by all of the other candidates, if there is such a
candidate ... Otherwise ...
1. let X be the candidate with the least PO to the candidate C whose Max PO
is smallest among the remaining candidates. Then
2. Eliminate X, as well as any candidate(s) covered by X relative to the
remaining candidates.
EndWhile

Finally, elect the sincere runoff winner between the two remaining
candidates.

Examples to follow soon ....

For now, we only mention that the eliminations are designed to make it
highly likely that when a sincere undefeated candidate exists; it will be
one of the finalists ... and also to point out that the elimination of
candidates covered by other candidates being eliminated ... this precaution
ensures that no covered candidate will be elected ... thus avoiding a
potential liability that plauges nearly all other extant methods.

fws
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