[EM] Intermediate RV rating is never optimal

[Chris Benham]

Abd ul-Rahman Lomax wrote:

>bits and pieces
>
>At 05:33 AM 7/21/2007, Michael Ossipoff wrote:
>  
>
>>That's incorrect. It's exactly the same in RV as in Approval. In 
>>your example, with B at your Approval cutoff, it doesn't matter how you rate B.
>>    
>>
>
>In what I wrote, B was not at the voters "approval cutoff." I didn't 
>give an approval cutoff. Approval cutoff is an artificial insertion; 
>it's a device for converting range ratings to approval votes.
>
>This is the situation described:
>
>The voter prefers A>B>C, with the preference strength between A and B 
>being the same as the strength between B and C.
>
>There is nothing here about Approval cutoff, there is nothing that 
>says that the voter does or does not "approve" of *any* candidate.
>

I think we safely say that max-rating a candidate is equivalent to 
"approving" that candidate.

>Ossipoff confused the fact that the candidate was intermediate 
>between A and C in sincere rating, i.e., being midrange, with being 
>"at your Approval cutoff."
>
If the preference strength between A and B is  weaker than that between 
B and C then with
the winning probabilities being equal (or unknown) then the voter's best 
strategy is to max-rate
A and B. If instead the preference strength between B and C is weaker, 
the voter does best to
min-rate B and C (and of course max-rate A).

Since the situation you describe is at the border of these two (max-rate 
B or min-rate B), we can
say that "B is at your approval cutoff".

>And, quite clearly, it *does* matter how 
>you rate B in some scenarios; for example, if the real pairwise 
>election is between A and B, then the optimum vote is to rate B at 
>minimum. And if it is between B and C, then the optimum vote is to 
>rate B at maximum.
>

Of  course it can "matter" after the fact, but with both possible "real 
pairwise elections" being
equally likely at the time of voting, in Abd's scenario it 
probabilistically makes no difference what
rating the voter gives B.

Chris Benham


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