I agree it's silly to create complicated rules for a two-slot ballot. But, though Forest didn't quite say so, I also think that FBC and (voted ballot) Condorcet are not incompatible for a 3-slot ballot.
Jameson 2011/11/22 Chris Benham <cbenha...@yahoo.com.au> > Forest, > > "When the range ballots have only two slots, the method is simply > Approval, which does satisfy the > FBC." > > When you introduced the method you suggested that 3-slot ballots be used > "for simplicity". > I thought you might be open to say 4-6 slots, but a complicated algorithm > on 2-slot ballots > that is equivalent to Approval ?? > > "Now consider the case of range ballots with three slots: and suppose that > optimal strategy requires the > voters to avoid the middle slot. Then the method reduces to Approval, > which does satisfy the FBC." > > The FBC doesn't stipulate that all the voters use "optimal strategy", so > that isn't relavent. > http://wiki.electorama.com/wiki/FBC > > http://nodesiege.tripod.com/elections/#critfbc > > Chris Benham > > > > > > *From:* "fsimm...@pcc.edu" <fsimm...@pcc.edu> > *To:* C.Benham <cbenha...@yahoo.com.au> > *Cc:* em <election-meth...@electorama.com>; MIKE OSSIPOFF < > nkk...@hotmail.com> > *Sent:* Tuesday, 22 November 2011 11:11 AM > *Subject:* Re: An ABE solution > > > > From: "C.Benham" > > > > > Forest Simmons, responding to questions from Mike Ossipff, wrote > > (19 Nov > > 2011): > > > > > > 4. How does it do by FBC? And by the criteria that bother some > > > > people here about MMPO (Kevin's MMPO bad-example) and MDDTR > > > (Mono-Add-Plump)? > > > > > > I think it satisfies the FBC. > > > > Forest's definition of the method being asked about: > > > > > Here’s my current favorite deterministic proposal: Ballots are > > Range > > > Style, say three slot for simplicity. > > > > > > When the ballots are collected, the pairwise win/loss/tie > > relations are > > > determined among the candidates. > > > > > > The covering relations are also determined. Candidate X covers > > > candidate Y if X > > > beats Y as well as every candidate that Y beats. In other > > words row X > > > of the > > > win/loss/tie matrix dominates row Y. > > > > > > Then starting with the candidates with the lowest Range > > scores, they are > > > disqualified one by one until one of the remaining candidates > > X covers > > > any other > > > candidates that might remain. Elect X. > > > > > > Forest, > > > > Doesn't this method meet the Condorcet criterion? Compliance > > with > > Condorcet is incompatible with FBC, so > > why do you think it satisfies FBC? > > When the range ballots have only two slots, the method is simply Approval, > which does satisfy the > FBC. Does Approval satisfy the Condorcet Criterion? I would say no, but > it does satisfy the "votes only > Condorcet Criterion." which means that the Approval winner X pairwise > beats every other candidate Y > according to the ballots, i.e. X is rated above Y on more ballots than Y > is rated above X. > > Now consider the case of range ballots with three slots: and suppose that > optimal strategy requires the > voters to avoid the middle slot. Then the method reduces to Approval, > which does satisfy the FBC. > > > > > > > > http://lists.electorama.com/pipermail/election-methods- > > electorama.com/2005-June/016410.html > > > > > 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. > > Note that in our method the Cardinal Ratings order (i.e. Range Order) is > needed in addition to the > pairwise matrix; the covering information comes from the pairwise matrix, > but candidates are dropped > from the bottom of the range order. > > In the two slot case can the approval order be determined from the > pairwise matrix? If so, then this is a > counterexample to the last quoted sentence above in the attempted proof of > the incompatibility of the CC > and the FBC. > > Forest > > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info > >
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