How about 1-2-2-2-2 or 2-2-3-3-3? If I figured right, the Borda count order changes when you remove the ties, and in the later case the winner changes (if I counted right, which may be a problem since I'm figuring it during a tech support call :)
Mike Rouse [EMAIL PROTECTED] ----- Original Message ----- From: "Adam Tarr" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Friday, March 29, 2002 12:37 PM Subject: Re: Saari and Cyclic Ambiguities > > >5: ABCDE > >6: BCDEA > >7: CDEAB > >8: DEABC > >9: EABCD > > The only ranked method discussed here that does NOT hand this election to E > is IRV. > > Borda count reduces this to > > 1: BCDEA > 2: CDEAB > 3: DEABC > 4: EABCD > > And the Borda scores are 20, 15, 15, 17, 30, for A, B, C, D, and E, > respectively. E wins by a huge margin. > > In Condorcet voting, the Smith/Schwartz set is every candidate, there are > no ties, and every voter expressed a full ballot. So all the Condorcet > methods are pretty much the same. Ranked pairs overturns D>E and C>E (in > that order). SSD drops C>E, B>D, D>A, A>C, E>B, and D>E, (in that > order). Both results leave E unbeaten. > > In IRV, A is eliminated first, then C, then E (by a count of 11B 15C > 9E). E gets screwed by having the wrong votes transfer. B wins the > election, even though B finished dead last in Borda Count and only beats > one candidate pairwise. > > If the Approval cutoff is consistent, then Approval elects E as > well. Plurality of course elects E as well. So really, only IRV can screw > this one up. It's not tremendously illustrative (sorry). > > -Adam >
