regret

[Mike Ositoff]

yesterday I mentioned regret minimization as a voting strategy
when nothing is known about winnability, but when one has
utility ratings.

Regret is measured by the utility difference between the person
who won & the best person whom you could have made to win
had you voted for him.

As I said, in Approval, when nothing is known about winnability
or tie probabilities, one minimizes possible regret by
voting down to the average of the best & the worst.

Say we designate the worst as 0 & the best ass 100. If you
vote down to 50, then, at worst, someone with 0 utilitly
will win, and you'll find out that you could have made someone
with 49 win. Or someone with 50 will win and you'll find that
you could have made your favorite, with 100, win had you
not voted for the 50 guy. Obviously, if you make your cutoff
point higher or lower, you increase the possible regret.

But when you have utility ratings, but no winnability knowledge,
then if I were a result optimizer, I'd instead vote to maximize
utility expectation by averaging _all_ the utilities, not
just the best & worst, & voting down to that average.

Mike