Forest: In your example,
>66 A>B>C >34 B>C>A If you give second preferences any more than 16/33 of the weight which you give to the first prefs, the winner is B; since: 34+66x=66 66x=32 x=32/66 x=16/33 Let's look at another example: 1,000,001 A>B>C 1,000,000 B>C>A 1,000,000+1,000,001x=1,000,001 1,000,001x=1 x=1/1,000,001 In this case, a second pref must be given less than 1/1,000,001 of the weight of a first pref, if A should win. That's a stretch. SB >===== Original Message From Forest Simmons <[EMAIL PROTECTED]> ===== >Here's an example with the symmetry already subtracted out. [Add it back >in and then subtract it out again if you want to.] > >66 A>B>C >34 B>C>A > >A should be the winner, but Borda picks B. > >Forest > >On Thu, 16 Jan 2003, Steve Barney wrote: > >> Forest: >> >> That's quite a strong claim you made there. I must have missed it. Please give >> me the number of the EM message in which you did what you describe below. >> >> SB >> >> >From: Forest Simmons <[EMAIL PROTECTED]> >> >To: <[EMAIL PROTECTED]> >> >Subject: RE: [EM] Saari's Basic Argument >> > >> >I've already given an example in which Borda gives the wrong answer after >> >the symmetry is removed. Now you have given an example in which symmetry >> >removal shows the CW to be wrong. So that evens the score :-) >> > >> >In other words, neither Borda nor Condorcet can claim to be superior on >> >the basis of symmetry removal. >> > >> >So here's a new method (for three candidate races only): first remove all >> >of the symmetry, and then the candidate with a majority of first place >> >votes (on the remaining ballots) is the winner. >> > >> >This method beats both Borda and Condorcet by the "symmetry removal >> >criterion." >> > >> >Forest Steve Barney Richard M. Hare, 1919 - 2002, In Memoriam: <http://www.petersingerlinks.com/hare.htm>. Did you know there is an web site where, if you click on a button, the advertisers there will donate 2 1/2 cups of food to feed hungry people in places where there is a lot of starvation? See: <http://www.thehungersite.com>. ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
