<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
<html>
<head>
<meta content="text/html;charset=ISO-8859-1" http-equiv="Content-Type">
</head>
<body bgcolor="#ffffff" text="#000000">
<br>
<br>
Abd ul-Rahman Lomax wrote:<br>
<blockquote type="cite">
<pre wrap="">
At 04:36 AM 7/26/2007, Michael Ossipoff wrote:
</pre>
<blockquote type="cite">
<pre wrap="">So I repeat that, in public elections, Schudy's statement was
correct, when he said that it is never optimal to rate someone other
than top or bottom.
</pre>
</blockquote>
<pre wrap=""><!---->
I have currently posted a counterexample. Perhaps Ossipoff addresses
it later, but prior to the present post he has not.
The example: many voters, large enough that a three-way tie is of
negligible effect on utilities.
Three candidates. Range 2 (CR-3).
Voter with utilities of 2, 1, 0.
Zero knowledge, so all vote patterns from the electorate minus our
voter are equally possible.
Expected utility of Approval Votes of 220 or 200: 39/27 (improvement
over not voting: 12/27).
Expected utility of Sincere Vote, 210: 40/27, improvement over not
voting: 13/27.
Improvement over Approval by voting Sincerely: 1/27.
Take a look. If there is an error in the calculation, I'd like to
know. </pre>
</blockquote>
<br>
What "calculation"? Look at what? With "many voters" your
"improvement over not voting"<br>
figures look too high. <br>
<br>
<blockquote type="cite">
<pre wrap="">Please, if you can, find the error in the proof; sufficient
information has been given as to how to do it, and my spreadsheet has
been posted, but you'll need Excel or some spreadsheet program that
can read Excel files.</pre>
</blockquote>
Right. "Posted" where?<br>
<br>
Chris Benham<br>
<br>
<br>
</body>
</html>