[EM] Does Bucklin 2-level satisfy Participation (mono-add-top)?

Ted Stern araucaria.araucana at gmail.com
Tue Jan 3 13:44:19 PST 2012

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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