This seems to be an open question at present. But it might be pretty easy to prove or disprove.
A multiwinner voting method "obeys participation" if an extra voter, by voting honestly, cannot make the election result worse (in her view) than if she had not voted. (If you remove a winner and replace it with somebody that voter considers better, the winner set got better. Any change in the winner set not arising from a finite sequence of such improvement steps, is a "worsening" in the view of some voter.) It is "fair" if symmetric under permuting the candidates and voters. Conjecture: there does not exist a fair multiwinner proportional representation voting method obeying participation. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step) and math.temple.edu/~wds/homepage/works.html ---- Election-Methods mailing list - see http://electorama.com/em for list info
