Dear James! I tried your example with "Random Ballot from Forest's P":
> 3 candidates: Kerry, Dean, and Bush. 100 voters. > Sincere preferences > 19: K>D>>B > 5: K>>D>B > 4: K>>B>D > 18: D>K>>B > 5: D>>K>B > 1: D>>B>K > 25: B>>K>D > 23: B>>D>K > Kerry is a Condorcet winner. > > Altered preferences > 19: K>D>>B > 5: K>>D>B > 4: K>>B>D > 18: D>K>>B > 5: D>>K>B > 1: D>>B>K > 21: B>>K>D > 23: B>>D>K > 4: B>D>>K (these are sincerely B>>K>D) > There is a cycle now, K>B>D>K With sincere votes, approval says B>K>D and defeats say B<K>D, hence we have R.B. from {B,K} so that Bush wins with 49%, Kerry wins with 51%. With altered votes, approval says B>D>K and defeats also say B>D>K, hence Bush wins with 100%. Seems bad, but nevertheless the strategy is risky and seems to depend on quite accurate guesses what the others will do: First of all, it would not have helped to vote 4: B>>D>K instead, since then approval still says B>K>D and defeats say B<K<D<B, hence we still have R.B. from {B,K} so that Bush still wins with 49%, Kerry wins with 51%. That is, the Bush voters must insincerely approve of their worst choice. Second of all, they must coordinate their strategy well, since when 6 or more instead of only 4 voters switch to B>D>>K, then approval says D>B>K and defeats say D<B<K<D, hence we have R.B. from {D,B} so that Bush wins now with 52%, but Dean wins with 48%. That is, when too many switch to the strategic voting pattern, they increase Bush's probability only slightly but transfer Kerry's probability to Dean! A similar effect happens when 2 of the 5 K>>D>B voters switch to K>D>>B as an anti-strategic measure. So, my impression is that although not as good as cardinal or approval weighted pairwise, this much simpler method still performs quite well in terms of strategy-proofness, do you agree? Yours, Jobst ______________________________________________________________ Verschicken Sie romantische, coole und witzige Bilder per SMS! Jetzt bei WEB.DE FreeMail: http://f.web.de/?mc=021193 ---- Election-methods mailing list - see http://electorama.com/em for list info