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

Jameson Quinn jameson.quinn at gmail.com
Tue Jan 3 16:38:56 PST 2012

```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 <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
> 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
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.electorama.com/pipermail/election-methods-electorama.com/attachments/20120103/35b8f910/attachment-0004.htm>
```