Kevin wrote: > Yes, but if it were strategy-free somehow, I think it would be worth > it. Real life isn't monotone. I don't imagine that all the prettier Yee > diagrams would really look like that if voters were using information > and strategy!
I may be missing something, but I don't see how you can have a nonmonotonic method that is strategy-free. For any example of nonmonotonicity, you should be able to find a single voter that triggers it--say, if that focal voter votes A>B>X>C, then X wins, but if they vote A>X>B>C, then X loses. Whoever wins when X loses, manipulability pops up: Case 1: A wins. Then imagine that the focal voter sincerely thinks A>B>X>C. Insincerely voting A>X>B>C moves the winner from X to A, which is a successful manipulation. Case 2: B wins. Then imagine that the focal voter sincerely thinks A>B>X>C. Insincerely voting A>X>B>C moves the winner from X to B, which is a successful manipulation. Case 3: C wins. Then imagine that the focal voter sincerely thinks A>X>B>C. Insincerely voting A>B>X>C moves the winner from C to X, which is a successful manipulation. This "proof" may be either flawed or needlessly complex, but it's what came to mind. -- Rob LeGrand [email protected] Citizens for Approval Voting http://www.approvalvoting.org/ ---- Election-Methods mailing list - see http://electorama.com/em for list info
