Hi Abd, and M. Smith if I understood well, I checked your spreadsheet.
You are missing the -1 cases for A. Thus the impact on the sincere ballot compared to the approval one is overestimated. Try again considering -1 , 0 and 1 as the three rests after removing your offset. You should find different results. The emperor is not naked, he is just not well dressed... S. Rouillon >From: Abd ul-Rahman Lomax <[EMAIL PROTECTED]> >To: [EMAIL PROTECTED] >Subject: [Election-Methods] Study Data,Personal Utility with Range 2 >election >Date: Thu, 26 Jul 2007 22:00:14 -0400 > >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 ---- Election-Methods mailing list - see http://electorama.com/em for list info