Hello Forest! Yesterday I wondered whether under Approval Voting there would always be some equilibrium of the following kind: All voters specify "sincere" approvals in the sense that when they prefer X to Y they do not approve of Y without approving of X; and no group of voters can improve their result by changing their specified approvals to some different but still "sincere" (!) set of approvals.
I hoped that such weak kinds of equilibria might exist always. Unfortunately, I get the impression that in the following example there is no such equilibrium: 3 D>C>A>B 3 D>A>B>C 5 A>B>C>D 4 C>B>D>A So, can someone specify a "sincere" way of voting which would be proof against "sincere" strategies in the above sense? For example, the following is not such an equilibrium: 3 D>C>>A>B 3 D>A>>B>C 5 A>B>>C>D 4 C>B>>D>A Here B wins, but 8 of the 11 voters which prefer A to B can switch to 3 D>C>A>>B 5 A>>B>C>D without voting "insincerely", but making A the winner. Also, the following is not an equilibrium of the desired kind: 3 D>C>>A>B 3 D>A>B>C (all or none approved) 5 A>B>C>>D 4 C>>B>D>A Here C wins, but the 8 voters which prefer A to C can switch to 3 D>A>>B>C 5 A>>B>C>D without voting "insincerely", but making A the winner. And so on... So, can anybody forecast what will happen with these preferences under Approval Voting?? 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
