On 03 Jan 2012 16:38:56 -0800, Jameson Quinn wrote: > > 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.
I have never heard of an ER-Bucklin method that did not use highest total threshold-level approval to pick the winner. I.e., if there is more than one candidate that has a total threshold-level approval above the quota, the highest total wins. If A wins with the first N votes, A could win either in the first level or second level round. If x A>B votes are added, then if A had won the pre-x vote in the first round, A would still win. If A had won the pre-x count only after dropping the threshold to the second level, then the addition of x A>B votes would be equivalent to adding the same number of A and B approvals to the second-level approval totals. Therefore if A had won pre-x, A would still win post-x. To answer Kristofer's point: in a two-level ER-Bucklin method, mono-add-top is the same as Participation, because there is no way to add A > B rankings without A having the maximum rating. Okay, thanks to both of you! That is encouraging ... that means that 2-level ER-Bucklin gets Steven Brams's seal of approval :-). Ted > 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 > -- araucaria dot araucana at gmail dot com ---- Election-Methods mailing list - see http://electorama.com/em for list info
