Jobst wrote: > 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 anybody forecast what will happen with these preferences > under Approval Voting??
Interesting example. Bucklin gives B, IRV gives D, Borda gives A and most methods popular here (beatpath, River, Ranked Pairs) give C. There is no Condorcet winner, so there is no Approval equilibrium; any leader will be quickly toppled if everyone uses strategy A (which is always sincere in the sense you give above). Strategy A allows individual voters to move the current result in the most advantageous direction with no notion of being part of a new majority coalition; new coalitions emerge naturally from the smart strategic moves. Declared Strategy Voting in ballot-by- ballot mode running for many rounds using Approval and strategy A elects them with approximate probabilities A 25.05%, B 12.99%, C 27.54% and D 34.42%. Rob LeGrand, psephologist [EMAIL PROTECTED] Citizens for Approval Voting http://www.approvalvoting.org/ __________________________________ Do you Yahoo!? Yahoo! Small Business - Try our new resources site! http://smallbusiness.yahoo.com/resources/ ---- Election-methods mailing list - see http://electorama.com/em for list info