[EM] Participation

[fsimmons at pcc.edu]

If I am not mistaken, both Bucklin and MMPO satisfy Perez' weak version of
Participation: if the winner changes when a ballot is added, then the old winner
was not ranked top on the added ballot.

I wonder if some kind of hybrid between these two methods might be better than
either without losing this form of Participation.

For one thing, the pairwise oppositions in MMPO would need to be replaced with
some kind of weighted pairwise opposition to ensure clone independence.  For
that we need two or more levels if not full blown cardinal ratings.  

What if the three levels are (1) anything from the top rank down to the level of
collapse that would be needed if Bucklin were used, (2) other ranked, and (3)
truncated?  Then if a ballot has x  in level 1, and y  in level 3, that ballot
contributes two to the opposition of x against y, whereas if x is only one level
above y, the ballot contributes only one to the opposition.

Any other thoughts on this?