[Election-Methods] Smith exposes our false statements

[Chris Benham]

Abd ul-Rahman Lomax wrote:

>At 04:36 AM 7/26/2007, Michael Ossipoff wrote:
>  
>
>>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.
>>    
>>
>
>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. 
>

What "calculation"?  Look at what?  With "many voters" your "improvement 
over not voting"
figures look too high. 

>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.
>
Right.  "Posted" where?

Chris Benham


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