Re: [EM] Does Bucklin 2-level satisfy Participation (mono-add-top)?
On 01/03/2012 10:44 PM, Ted Stern wrote: 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) Mono-add-top is not the same thing as Participation. IRV passes the former but fails the latter (to my knowledge). Consider a method where, given a certain ballot set, A wins, that the method's social ordering is A C B D, and that no A-top vote can change the winner. Then someone comes along and votes B A C D. After he does so, the winner switches to C. Then that method fails Participation (because the voter who submitted that ballot expressed A C yet the method switched from A to C), but not mono-add-top (because B A C D is not an A-first ballot, and it didn't harm B's relative position in the ordering because B wasn't a winner anyway). That said, I am not aware of any examples where two-level Bucklin fails either Participation or mono-add-top. If the voters have to rank every candidate and have only two levels, then I think Bucklin always gives the same result as Approval (in which case it would pass both). With truncation, however, it gets more murky. Election-Methods mailing list - see http://electorama.com/em for list info
Re: [EM] Does Bucklin 2-level satisfy Participation (mono-add-top)?
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, AB 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 AB 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 AB 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 araucaria.arauc...@gmail.com 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
[EM] Does Bucklin 2-level satisfy Participation (mono-add-top)?
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
Re: [EM] Does Bucklin 2-level satisfy Participation (mono-add-top)?
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, AB votes can cause BA (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 araucaria.arauc...@gmail.com 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 Election-Methods mailing list - see http://electorama.com/em for list info
