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

[Kevin Venzke]

Hi,

I've now looked at your work, and I believe you have shown that when
your value of a candidate is exactly equal to your expectation from the
election, then if the midrange rating is available to you, that is the
rating you should use. At least some of the time it is better and it
should never be worse.

I believe you asked then, following this conclusion, what resolution
gives the voter the most ability to improve his expectation. The answer
would be that three slots are sufficient. I can't see what more you could
ever gain from five or seven slots, since all you ever need to use is 
the midpoint.

For example, if your expectation is 1.0 and your values for the 
candidates are 2.0, 0.9, and 0.0, you would not optimally round that 0.9 
to a 1 rating. You would only use the 1 rating when there is no expected
difference between rating 0 or 2 for that candidate.

In my simulation, I am sure there would be no perceptible difference if
I converted our voter's ratings into three-slot ratings for voting
purposes, since it is quite rare for a candidate's value to be precisely
at the mean when you have such high resolution for your sincere values.

On the other hand, if internally you do rate candidates using integers
from 0 to 2 inclusive, it is much more likely that it could happen that you
would want to use the 1 rating.

I must emphasize that it's not that sincerity is optimal in zero-info
three-slot range elections. The optimal vote only happens to be sincere
in the situation you examined. Similarly it can happen that an approval
vote formed according to some other strategy is both optimal and sincere.

Kevin Venzke


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