Hi Mike, --- En date de : Jeu 27.10.11, MIKE OSSIPOFF <[email protected]> a écrit : > I'd said: > > > There is only one candidate B. It would be nice if > {A,B} > > could be replaced > > with a larger set of candidates, but the crierion > would > > then probably be > > unattainable. > > [unquote] > > You wrote: > > By allowing multiple "B" candidates, my criterion is > stronger than > yours, and it is attainable. > > [unquote] > > By what method? > > If you're right, that's good news. > > I don't deny that yur criterion is stronger. I merely > question whether > it's attainable.
I should say, I am starting to have a doubt as to whether my criterion does everything I think it does. But it is stronger than yours and should do what you want. The simplest method I am proposing that satisfies your criterion is MDD//Condorcet//Approval, let's say. > > You had said: > > > > As far as methods that will satisfy it, we at least > have > > some clumsy > > ones. Any Condorcet method used to complete > > majority-defeat- > > disqualification or CDTT (i.e. Schwartz set that > replaces > > sub-majority > > wins with ties) will do the trick. These methods would > also > > satisfy > > SDSC fully. > > > > [endquote] > > I'd replied: > > > Worth checking out. But, even if you're correct about > that, > > how many of those methods > > meet FBC? > > You write: > > None of them satisfy FBC, but neither does your version of > MMPO. > > [endquote] > > As has already been asked, do you have an FBC failure > example for MMPO? > > Do you mean that, by ranking a compromise over your > favorite, you could get > the compromise into a tie, by lessening the compromise's > pairwise opposition and > increasing your favorite's pairwise opposition--Where > otherwise your favorite would > go into the tie and lose? > > Can you show an example? I will try to think of one but it won't be easy, I don't think... > I'd said: > > > Can those methods be shown to meet CD? Of course, the > > burden of proof, in the > > form of a failure example, is on the person claiming > that > > they don't. ...because it's > > often easier to show noncompliance than compliance. > But > > even so, what method other > > than MMPO can be shown to meet CD? > > [endquote] > > > I am quite confident I can convince you that my > above-listed methods > satisfy CD. > > Try this method: > 1. If possible, eliminate every candidate with a majority > loss > 2. If there is a CW among remaining candidates, elect him > 3. Otherwise elect somebody arbitrarily (doesn't matter) > > Isn't it pretty clear that this meets your criterion? > > [endquote] Ok, let me try to prove to you tha this method satisfies your criterion. In the scenario you're talking about, on the cast ballots: A will have at least a simple win over B A will not have a majority loss to C B will definitely have a majority win over C MDD//Condorcet//Approval will disqualify C and will not definitely not disqualify A. So the only question is whether B, if he is not disqualified, can beat A. Impossible, because A has a pairwise win over B and is the CW of those candidates. Have I ignored any other factors? By the way, I am a bit confused on one aspect of what you've told me. You said it isn't necessarily true that A has a *majority* win over B. I thought A must have a majority because the B voters will be the only ones not voting A>B, and the B voters certainly are not a majority. If that's not true though, so that some *C* voters are also not voting A>B, then the method really can't be sure whether the CW is A or B. In that case, a method can pick the pairwise winner between A or B, but it can't promise which one is sincere CW, so your criterion would be totally unattainable. I think you need to require that B cannot possibly be the sincere CW. > I feel that FBC is more important than CD. > > If I had to choose between FBC and CD, I'd choose FBC. > > If solve-its-own-ties MMPO (which is what I mean by MMPO) > can be shown to fail FBC, then I'd drop it. > > But, by the same token, do your CD-complying methods meet > FBC? > > If MMPO fails FBC, can you suggest a method that meets FBC, > SFC &/or SDSC, and CD? > > Can CD be shown to be incompatible with FBC? My CD-complying methods do not satisfy FBC. (I can't prove it at the moment, but it would make no sense to me that they do.) I strongly suspect that in order to satisfy CD, methods must use something that looks or acts like a Condorcet mechanism or beatpath mechanism, and would as a side effect fail FBC. I don't believe I can prove that they are not compatible though. Kevin ---- Election-Methods mailing list - see http://electorama.com/em for list info
