[EM] Try this method on your favorite election scenario

Forest Simmons fsimmons at pcc.edu
Sun Oct 6 15:21:35 PDT 2013

Ballots are ranked or rated.  If ranked, then equal ranking and truncation
are allowed.

Let IA stand for Implicit Approval, which for any candidate X is the number
of ballots on which X is ranked or rated above bottom, i.e. neither
truncated nor rated at zero.

Let MPO stand for maximum pairwise opposition, which (for candidate X) is
the maximum (as Y varies over the other candidates) of the number of
ballots on which a strict preference of Y over X is indicated.

The winner of this method (IA/MPO) is the candidate with the highest ratio
of IA to MPO.


45 A>B
35 B>C
20 C

For A  IA is 45 and MPO is 55, so IA/MPO is 45/55 or 9/11.
For B IA is 80 and MPO is 45, so IA/MPO is 80/45 or 16/9.
For C IA is 55 and MPO is 80, so IA/MPO is 55/80 or 11/16.

The IA/MPO winner is B.

If, instead, the A faction votes 45 A, then the ratios become ...

For A  (the same) 9/11.
For B  IA is 35 and MPO is still 45, so the ratio is 7/9.
For C IA is still 55 and MPO is 45, so the ratio is 11/9.

This time C wins.
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