I don't agree that "Sincere Favorite" is practically equivalent to the FBC. The FBC is about not having to lower your one favorite candidate; it is not about not having to pick a single favorite from your favorite set. As a voter, I'd regard the former as a serious dilemma, and the latter as a trivial detail.
Jameson 2011/11/23 Chris Benham <cbenha...@yahoo.com.au> > Forest, > > > "Furthermore something must be wrong with the quoted proof (of the > incompatibility of the FBC and the > CC) because the winner of the two slot case can be found entirely on the > basis of the pairwise matrix." > > The likely explanation for some odd remarks by you and Jameson has just > occurred to me. Could it be > that you and Jameson have mistaken a set of ballots for a "pairwise > matrix" ?? > > Here is that quoted proof again, with the ballots represented in the more > familiar EM notation: > > Hello, > > This is an attempt to demonstrate that Condorcet and FBC are incompatible. > I modified Woodall's proof that Condorcet and LNHarm are incompatible. > (Douglas R. Woodall, "Monotonicity of single-seat preferential election > rules", > Discrete Applied Mathematics 77 (1997), pages 86 and 87.) > > I've suggested before that in order to satisfy FBC, it must be the case > that increasing the votes for A over B in the pairwise matrix can never > increase the probability that the winner comes from {a,b}; that is, it must > not move the win from some other candidate C to A. This is necessary > because > if sometimes it were possible to move the win from C to A by increasing > v[a,b], the voter with the preference order B>A>C would have incentive to > reverse B and A in his ranking (and equal ranking would be inadequate). > > I won't presently try to argue that this requirement can't be avoided > somehow. > I'm sure it can't be avoided when the method's result is determined solely > from the pairwise matrix. > > Suppose a method satisfies this property, and also Condorcet. Consider > this > scenario: > > 3: A=B > 3: A=C > 3: B=C > 2: A>C > 2: B>A > 2: C>B > > There is an A>C>B>A cycle, and the scenario is "symmetrical," as based on > the submitted rankings, the candidates can't be differentiated. This means > that an anonymous and neutral method has to elect each candidate with > 33.33% > probability. > > Now suppose the a=b voters change their vote to a>b (thereby increasing > v[a,b]). > This would turn A into the Condorcet winner, who would have to win with > 100% > probability due to Condorcet. > > But the probability that the winner comes from {a,b} has increased from > 66.67% > to 100%, so the first property is violated. > > Thus the first property and Condorcet are incompatible, and I contend that > FBC > requires the first property. > > Thoughts? > > Kevin Venzke > > > http://lists.electorama.com/pipermail/election-methods-electorama.com/2005-June/016410.html > > It is certainly a clear proof of the incompatibilty of the Condorcet > criterion and Kevin's later > suggested "variation" of the FBC, "Sincere Favorite": > > *Suppose a subset of the ballots, all identical, rank every candidate in > S (where S contains at least two candidates) equal to each other, and above > every other candidate. Then, arbitrarily lowering some candidate X from S > on these ballots must not increase the probability that the winner comes > from S.* > A simpler way to word this would be: *You should never be able to help > your favorites by lowering one of them.* > > http://nodesiege.tripod.com/elections/#critfbc > I can't see any real difference between this and regular FBC, which > probably partly explains > why it didn't catch on. > > Chris Benham > > > *From:* "fsimm...@pcc.edu" <fsimm...@pcc.edu> > *Sent:* Wednesday, 23 November 2011 9:01 AM > > *Subject:* Re: An ABE solution > > You are right that although the method is defined for any number of slots, > I suggested three slots as > most practical. > > So my example of two slots was only to disprove the statement the > assertion that the method cannot be > FBC compliant, since it is obviously compliant in that case. > > Furthermore something must be wrong with the quoted proof (of the > incompatibility of the FBC and the > CC) because the winner of the two slot case can be found entirely on the > basis of the pairwise matrix. > The other escape hatch is to say that two slots are not enough to satisfy > anything but the voted ballots > version of the Condorcet Criterion. But this applies equally well to the > three slot case. > > Either way the cited "therorem" is not good enough to rule out compliance > with the FBC by this new > method. > > Indeed, the three slot case does appear to satisfy the FBC as well. It is > an open question. I did not > assert that it does. But I did say that "IF" it is strategically > equivalent to Approval (as Range is, for > example) then for "practical purposes" it satisfies the FBC. Perhaps not > the letter of the law, but the > spirit of the law. Indeed, in a non-stratetgical environment nobody > worries about the FBC, i.e. only > strategic voters will betray their favorite. If optimal strategy is > approval strategy, and approval strategy > requires you to top rate your favorite, then why would you do otherwise? > > Forest > >
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