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

[Abd ul-Rahman Lomax]

At 09:17 AM 7/27/2007, Kevin Venzke wrote:
>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.

It turns out that it is not better, it is the same as approval. It 
will be interesting to see if this holds for other combinations where 
an exact Range vote is possible. It may turn out, indeed, that 
overall utility maximization occurs with hi-res range. The 
speculation that it did not was based on an incorrect list of vote 
possibilities and a resulting error in utility calculations.

It is now possible, with this technique, to study Range N and find 
*exact* expected utilities for particular candidate utility patterns 
and vote patterns. It will be interesting to see how that plays out 
as we increase N.

>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.

That's only true if the utility of a candidate falls at the midpoint. 
My next study would be Range 3 with the candidate utilities being 3, 
2, 0. What happens?

And what happens if we take the Range election and change it to an 
approval election by only allowing the vote patterns that can occur 
in approval. It's a trivial change to the spreadsheet. Does it affect 
the utilities?

>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.

That seems to be correct. However, I can easily test it. My guess is 
that error in specifying utility will create error in maximizing 
utility. What is the exact effect?

And, suppose that changing the election to Approval worsens expected 
utility? It is certainly logically possible, with what we know so 
far, that approval voting strategy is the best strategy, but shifting 
to approval as a method lowers the voter's expectation. Is this true, or not?

Remember, I now think I know the answer. But, of course, I've been 
wrong before. The nice thing about this is that it's not some 
abstract discussion. I'm talking about simple math, and simple math 
errors can usually be found!

>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.

This would lead to some conclusion about optimal Range. Humans don't 
really maintain very precise comparative utilities, and there is a 
lot of noise in them. But this is a fuzzy question. Right now I'm 
really interested in questions that can be answered definitively.

>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.

Yes. I'm not making any general claims as yet, beyond the *exact* 
claim I stated.

There is another factor, also hard to quantify. There is a utility 
routinely assigned by most (healthy) humans to honesty, sincerity, 
full and open disclosure. Thus a more complete utility analysis could 
cause loss of utility through sincere voting (which now appears to be 
related to error in the vote, but that's still speculative for me), 
but would still consider the sincere vote to be optimal.

And given that the sincere vote *does* beat approval in overall 
public utility (which can be known in simulations, they are assumed, 
not derived from the voters, rather the votes are derived from the 
utilities), there is an additional motivation for sincere voting: it 
is of overall public benefit.

When I have answered the question about shifting the election from 
Range to Approval, and the effect on utility, we will be in a better 
position to start evaluating election methods with this technique. 
It's still too soon.

What I've been saying in this thread is that the optimal vote depends 
on the original utility pattern and on election probabilities.... 
that continues to be true.