http://www.beyondpolitics.org/OptimalRangeVote.htm
Look at the last sheet. If your browser has trouble with the formatting, there is a simple page at http://www.beyondpolitics.org/OptimalRangeVote_files/sheet006.htm That page and the previous tab, sheet005, are reformatted for clarity, the other pages are my original 2-voter study and the first arrangement of the many-voter study. The election is many voters, so many that three-way ties can be neglected. The study looks only at conditions where the voter's vote can affect the outcome; conditions other than these cannot affect the voter's relative utilities for choices which *can* affect the outcome. (The utility for all those other conditions is 1.0 in this election.) This election is a counterexample to the claim that optimal voting in Range is never the sincere vote. The election is many voters, Range 2 (3 Cardinal Ratings), three candidates, zero knowledge. The voter has utilities of 2, 1, 0. The *relative* utility for voting sincerely is 40/27, for voting Approval Style, either 220 or 200, it is 39/27. Numerous writers have informed me that this is impossible, but have given me theoretical arguments which do not address the conditions of this study. Most notably, this is a Range 2 election, and it is totally zero knowledge, and the utilities are exactly balanced for the middle candidate. ---- Election-Methods mailing list - see http://electorama.com/em for list info
