Dear Steve Eppley, the following criterion has been discussed several times in the Election Methods mailing list:
Suppose a majority of the voters prefers candidate A to candidate B. Then candidate B must not be elected, unless there is a sequence of candidates from candidate B to candidate A where each candidate beats the next candidate with a majority that is at least as strong as the majority of candidate A against candidate B. The above criterion was called e.g. "beatpath criterion" or "immunity from binary arguments". The above criterion is satisfied e.g. by the Schulze method. Your "immunity from majority complaints" criterion has the following problems: (1) To guarantee that only the ranked pairs method satisfies this criterion, you added the requirement that each candidate of this sequence must be ranked ahead the next candidate of this sequence according to the social ordering. (2) To guarantee that only the ranked pairs method with "winning votes" satisfies this criterion, you added the requirement that the strength of a pairwise comparison must be measured by the number of voters who prefer the winning candidate to the losing candidate of this pairwise comparison. These additional requirements are not justified by the original motivation for this criterion: > Suppose a majority rank x over y but x does not > finish ahead of y (in the election's order of finish). > They may complain that x should have finished ahead > of y, using "majority rule" as their argument. (...) > So it is desirable to be able to turn their own > "majority rule" argument against them. (3) Your criterion presumes that the purpose of an election method is to create a social ordering. However, most readers will argue that the purpose of an election method is to find a winner and not to create a social ordering. Markus Schulze ---- Election-Methods mailing list - see http://electorama.com/em for list info
