This continues a thread that began last April with http://lists.electorama.com/htdig.cgi/election-methods-electorama.com/2010-April/025841.htm
Rivest confessed in his paper his method is not monotone. Here's a closely related method that is monotone: Voters submit ordinal ballots. Two game theorists that have no interest in the outcome of the election, but are compulsive gamblers, are enlisted to help decide the outcome. Without seeing any of the ballots, but after getting as much other information as they can amass by discreet indagations, both gamblers bet as to who will win the election. If they bet on the same candidate, that candidate wins. If they bet on different candidates, the winner is decided by random ballot between the two candidates, and the gambler who bet on the winner is declared winner of the bet. The method satisfies the FBC, is monotone, clone proof, Independent from non-Smith alternatives, Independent from Pareto Dominated Alternatives, etc. This shows that it is possible to have a method with all of the compliances that you would ever want, including Condorcet efficient and zero incentive for insincere ballots, provided that you are not wed to determinism. How does it accomplish this? Exactly like Approval accomplishes all of its great compliances; it externalizes the strategic manipulation. The manipulation can only happen when the two game theorist gamblers are inquiring around for information. That is when it might be to your advantage to lie to them, i.e. to not answer their questionnaires truthfully. The same thing happens in Approval. If you are going to vote optimally on an approval ballot, you need to gather information ahead of time. That is where all of the bluffing takes place. Rivest's method is a DSV (Designated Strategy Voting) version of the game I have described. No wonder it is non-monotone; we cannot even come up with a monotone DSV version of Approval. In my next message I will propose a general method for making monotone DSV methods from base methods that are monotone only by virtue of their externalizing the strategic part of the election. But for now, I would rather have you digest what I have presented so far. Forest ---- Election-Methods mailing list - see http://electorama.com/em for list info
