Dear Abd ulRahman! You wrote: > I'll disagree that "only randomized methods can do so," since there are > other alternatives that are neither deterministic or randomized, > beginning with the simple one of holding some kind of runoff.
Assume there is no sincere CW. Then each candidate is defeated by some other. You suggest runoffs which count as deterministic in the sense that the *whole* procedure will produce a single winner which depends only on the ballots cast. I claimed there cannot be a group strategy equilibrium in that case, that is, a way of voting such that after the election there is no group of voters who can say 'If only we had voted like so-and-so, we had the result so-and-so which we all prefer to the result at hand'. It's quite easy to see that such an equilibrium does not exist: Assume the whole election process elected X, and that X is defeated by Y. Then the majority which prefers Y to X can say 'If only we had voted Y>rest, we had the result Y which we all prefer to the result at hand'. QED. > Perhaps someone could take Mr. Heitzig's mail, with its concise > definition, and use it to clean up the wiki page. I'd do it if I had time. Please not "clean up" the page "imagine democratic fair choice" but add a new page "democratic fair choice". That was the whole point of my naming of the page. The idea is to have different descriptions for different tastes. Yours, Jobst ---- Election-methods mailing list - see http://electorama.com/em for list info
