In his last message Juho gave an example in which MinMax(wv) fails to satisfy the weak participation criterion that Perez said was satisfied by MinMax. I looked up Perez' proof, and found that he made essential use of complete rankings, in which case margins and wv give the same results. Joho's example involved truncations.
Investigating further I found that MinMax(AMP) [with approval determined from ranking versus truncation] also fails Perez' weak form of participation, but it does satisfy the following version of participation: If additional ballots are added, the new winner must be the old one or someone else that is approved (i.e. ranked) on at least one of the new ballots. This is the exact form of Participation that Approval satisfies, so we can claim that MinMax(AWP) (with approval determined by ranking versus truncation) satisfies Participation as well as Approval does. I do not know if Beatpath, River, or Ranked Pairs satisfies this form of Participation. ---- Election-Methods mailing list - see http://electorama.com/em for list info
