Sorry if I was not clear enough. All the comments I made were relevant only to truncation strategies... As you just showed, order reversal (burying for the intimates) can get even a strong Condorcet winner.
Two analysis could help go further in that direction: - Is there some level that makes a Condorcet winner immune to burying strategy ? - What is the method that brings the less esperance (gain probability) when using truncation or burying strategies? My guess would be that a stronger Condorcet winner (66% of winning votes) is immune to any strategy. Please feel free to show I am wrong... For the second analysis, I have not found any track toward a result yet. Bye, Steph. PS: Mike Ossipoff provides some proof for the 50% barrier immunity against truncation on some website. For the 66%, it is the result of my own analysis, and I do not have a formal proof. I do not know of any book containing such information. The last claim about no method protecting a weak Condorcet winner is obvious to me in the sense that any change of mind can bring different majorities, both leading to a legitimate winner. Again, I have no formal proof. Sorry for the lack of thourougness. > > De: Andrew Myers <[EMAIL PROTECTED]> > Date: 2005/09/13 mar. AM 12:19:55 GMT-04:00 > À: Stephane Rouillon <[EMAIL PROTECTED]> > Cc: [email protected] > Objet: Re: [EM] Citation for immunity to strategic voting? > > 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
