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

Kristofer Munsterhjelm km_elmet at lavabit.com
Wed Jan 4 06:50:29 PST 2012

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.

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