It depends on the "tiebreaker" used when there is are multiple majorities at second level. If the tiebreaker is that the most second-level votes wins, then I believe that the method meets participation. Otherwise, A>B votes can cause B&A (instead of just A) to pass the second-level threshold and trigger the tiebreaker; and B could win the tiebreaker.
Jameson 2012/1/3 Ted Stern <[email protected]> > I've seen examples in which Bucklin (with equal ratings) fails the > Participation criterion, AKA Woodall's mono-add-top criterion for > deterministic methods: > > "the participation criterion says that the addition of a ballot, > where candidate A is strictly preferred to candidate B, to an > existing tally of votes should not change the winner from candidate > A to candidate B." (from Wikipedia) > > In a Bucklin single-winner election with 3 or more levels, it is > possible that in an election in which the quota is not met at the > first or second level threshold, candidate A may be selected after the > threshold has dropped to the third level, but after adding some number > of A > B ballots, B then has enough votes to exceed the quota at the > second threshold, thus failing Participation. So the extra A > B > voters might as well have not shown up. > > However, if there are only two approval levels in the Bucklin > election, it appears that this problem could not occur, and the > no-show paradox would be avoided. The failure above hinges on the > fact that lower-ranked B fails to make quota at the 2nd level before > the new ballots are cast, but exceeds the quota afterward. With > levels compressed to two instead of three, B would exceed the quota at > the second level threshold initially. > > [Chris Benham has made me aware that ER-Bucklin 2-level still fails > the Independence of Irrelevant Alternatives, but that is a different > situation.] > > Does anyone know of any 2-level ER-Bucklin Participation failures? > > Ted > -- > araucaria dot araucana at gmail dot com > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info >
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