On Sun, Sep 11, 2005 at 04:47:19PM -0400, Andrew Myers wrote: > On Mon, Sep 05, 2005 at 05:55:01PM -0400, Stephane Rouillon wrote: > > Actually as many people will tell you, > > this claim is wrong. > > > > I see that Rob already gave you a counter example. > > > > Maybe you would like to know that using winning vote as > > criteria to make pairwise comparison instead of margins > > can make your claim true for strong Condorcet winners > > (ones which have a more than 50% majority against every > > other candidate).
Actually even this weaker claim (as I understand it) is wrong. Consider the following election with 100 voters: 23 A>B>C 25 A>C>B 3 B>A>C 26 B>C>A 3 C>A>B 20 C>B>A Therefore we have A preferred to B 51-49, A preferred to C 51-49, and B preferred to C 52-48. So A is a strong Condorcet winner. But consider what happens when the 3 B>A>C voters decide to bury A, changing their ballots to B>C>A. Then a cycle results: A vs. B: 51-49 B vs. C: 52-48 C vs. A: 52-48 According to all wv methods, we drop the weaker A vs. B preference, and B wins. -- Andrew ---- Election-methods mailing list - see http://electorama.com/em for list info
