[EM] Does Bucklin 2-level satisfy Participation (mono-add-top)?
araucaria.araucana at gmail.com
Wed Jan 4 16:16:20 PST 2012
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
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 :-).
> 2012/1/3 Ted Stern <araucaria.araucana at 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
> Does anyone know of any 2-level ER-Bucklin Participation failures?
> araucaria dot araucana at gmail dot com
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