[Election-Methods] Study Data, Personal Utility with Range 2 election

[Abd ul-Rahman Lomax]

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.