Mathematical utility expectation maximization in Approval

[Richard Moore]

Bart Ingles wrote:

> It should be pointed out that this entire discussion is more-or-less
> academic unless you plan to use the formulae to model strategy in
> simulations, based on randomly generated utilities or some such.  This
> is because in the real world, utility is determined by the willingness
> of a voter to vote for a candidate, and not the other way around.

I agree: The discussion is academic. It is an important one, though, because
the strategic differences between election methods, both in a zero-info
environment and otherwise, have consequences for the desirability of
the election methods themselves. For example, one thing I noticed is that
the zero-info strategies for IRV and Condorcet are identical: vote sincerely.
But start basing your strategy on outside information and wild things start
to happen, at least in IRV. It would be interesting to see what a non-ZI
strategy analysis for IRV tells us. One thing I can predict with a fair amount
of certaintly is that IRV is not reliable for increasing the aggregate utility
expectation, whether voters use a ZI strategy or not.

> If you are a voter attempting to assign utilities to candidates for the
> purpose of devising a strategy, remember that these assigned 'utilities'
> are really just ratings -- surrogates for real utilities.  Thus the
> 'neural net' approach is probably the more accurate (although
> calculations involving ratings might help to get you into the ball
> park).

Yes, I like the neural net approach myself (especially compared to
a non-ZI strategy -- because the calculations will be complicated).
We know (in approval anyway) whether voting for candidate X is the
Right Thing or not, so we intuitively know the value of voting a specific
way. But on some level the utilities exist. By that I mean that, if you
could explore a voter's response to outside information, you could, in
principal, estimate his utilities, even if he was unaware that he had them.

 -- Richard