You are right. It does avoid a favorite betrayal incentive if there is a sincere Condorcet winner, but not if there isn't.
Jameson 2011/11/9 C.Benham <[email protected]> > ** > Jameson, > > In response to Forest asking if there was a method that satisfies > something plus FBC you > responded: > > Yes. 321 voting > <http://wiki.electorama.com/wiki/321_voting><http://wiki.electorama.com/wiki/321_voting> > > > > 321 voting > From Electowiki > Jump to: navigation <#1338b9e6e791e9cc_column-one>, > search<#1338b9e6e791e9cc_searchInput> > > 3-level rated ballots. Of the 3 candidates with the most ratings, take the > 2 candidates with the most top-ratings, and then take the 1 pairwise winner > among those. > > > This fails FBC in the same way that ER-IRV(whole) does. From my 2 Nov. EM > post: > > <snip> > > Here is Kevin Venzke's example from a June 2004 EM post: > > 6: A > 3: C>B > 2: C=B (sincere is C>B) > 2: B > > The method is ER-IRV(whole). If the 2 C=B voters sincerely vote C>B then > the first-round scores are > A6, C5, B2. B is eliminated and A wins. > > As it is the first-round scores are A6, C5, B4. B is still eliminated > and A wins. > > To meet FBC no voters should have any incentive to vote their sincere > favourite below equal-top. > > 6: A > 3: C>B > 2: B>C (sincere is C>B) > 2: B > > But if those 2 voters (sincere C>B, was C=B) do that and strictly > top-rank their compromise candidate B, then the first-round scores are > A6, B4, C3. C is eliminated and B wins: B7, A6. > > By down-ranking their sincere favourite those 2 voters have gained a > result they prefer that they couldn't have got any other way, a clear > failure of the > Favorite Betrayal Criterion (FBC). > > <snip> > > Even if 321 voting met FBC with 3 candidates it it wouldn't with more, > because > sincerely rating your sincere favourite Top instead of Bottom could mean > that your > favourite displaces your compromise candidate from the top 3 most rated > candidates and > goes on to lose when your compromise would have won. > > Chris Benham > . > > > Forest Simmons wrote (9 Nov 2011): > > I'm assuming "approval bad example" is typified by the implicit approval > order in the scenario > > 49 C > 27 A>B > 24 B > > It seems to me that IF we (1) want to respect the Plurality Criterion, (2) > discourage "chicken" strategy, > (3) stick with determinism, and (4) not take advantage of proxy ideas, > then our method must allow > equal-rank-top and elect C in the above scenario, but elect B when B is > advanced to top equal with A in > the middle faction: > > 49 C > 27 A=B > 24 B > > Then if sincere preferences are > > 49 C > 27 A>B > 24 B>A, > > the B faction will be deterred from truncating A. While if the B > supporters are sincerely indifferent > between A and C, the A supporters can vote approval style (A=B) to get B > elected. > > Do we agree on this? > > Note that IRV (=whole) satisfies this, but now the question remains ... is > there a method that satisfies > this which also satisfies the FBC? > > Forest > > > > > > >
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