In fact, that would seem to be a pretty strong argument that these methods don't meet the FBC. What am I missing?
2012/1/24 Jameson Quinn <[email protected]> > The problem with these methods is that you can't afford to vote for the > marginal candidate whom only you have heard of, because that candidate will > not be part of any S, and so your ballot will count against any S, even an > S that you otherwise like. > > Jameson > > 2012/1/24 C.Benham <[email protected]> > > Following on from my recent definition of the APPMM criterion/set, I'd >> like to propose two not bad 3-slot methods that meet the FBC.. >> >> Recall that I defined the APPMM criterion thus: >> >> *If the number of ballots on which some set S of candidates is voted >>> strictly above all the candidates outside S is greater than the number of >>> ballots on which any outside-S candidate is voted strictly above any member >>> of S, then the winner must come from S.* >>> >> >> >> The APPMM set is the set of candidates not disqualified by the APPMM >> criterion. >> >> APMM//TR: >> >> * Voters fill out 3-slot ratings ballots. Default rating is Bottom >> (signifying least preferred and not approved.) The other slots are Top >> (signifying most preferred) and Middle. >> >> From the set of candidates not disqualified by the APPMM criterion, elect >> the one with the most Top ratings.* >> >> >> APMM//CR: >> >> * Voters fill out 3-slot ratings ballots. Default rating is Bottom >> (signifying least preferred and not approved.) The other slots are Top >> (signifying most preferred) and Middle. >> >> From the set of candidates not disqualified by the APPMM criterion, elect >> the one with the highest Top minus Bottom ratings score.* >> >> >> So far I can't see that these are technically any better than my earlier >> suggestion of TTPBA//TR, and unlike that method they fail the "Tied at the >> Top Pairwise Beats All" criterion. >> >> But like that method they meet the Plurality and Mono-add-Plump >> criteria, and also have no problem with Kevin's bad MMPO example. >> >> I'm happy for APMM//CR to be also called APMM//Range. This method is more >> Condorcetish than APMM//TR, for example: >> >> 49: C>B >> 27: A>B >> 24: B>A >> >> B>A 73-27, B>C 51-49, A>C 51-49. >> >> APMM//TR elects A, while APMM//CR elects B (like TTPBA//TR). >> >> I am sure that APMM//TR has no defection incentive in the "Approval Bad >> Example", and the other method also does in the example normally given. >> >> Of course some other points-score scheme (perhaps giving greater weight >> to to Top Ratings) is possible. >> >> Chris Benham >> >> >> >> >> ---- >> Election-Methods mailing list - see http://electorama.com/em for list >> info >> > >
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