Mathematical utility expectation maximization in Approval

[MIKE OSSIPOFF]

Bart 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.

That isn't always so. I calculated how I'd vote if I'd voted
in the San Francisco mayoral election. I estimated the Pij from
win probability estimates, and, for the candidates' utilities,
I used my best estimate of my sincere ratings of them.

Yes, one could work the other way, and calculate utilities from
how one chooses among lotteries or how one votes. Or one could
start by estimating sincere ratings, utilities, and then use those
and the Pij to calculate how to vote.

>
>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.

There's a notion that the only "real utilities" are vNM utilities,
utilities calculated from how we'd choose in a lottery . No, the word 
"utility" was being used, centuries before von Neuman or Morgenstern were 
born, to mean how good you rate something to be, or how valuable you rate it 
to be.

Yes, von Neuman & Morgenstern suggested that utilities can be
estimated from lottery choices. Yes, utilities estimated in that
way might be different from the sincere ratings that you estimate
if someone asks you to rate the candidates. No, the vNM utilities
aren't somehow more correct than the sincere ratings. No, utilities
doesn't mean vNM utilities.

When I did the SF mayoral election, I used my sincere ratings of the
candidates. In previous discussions, I've pointed out that that's
the way of voting that will look best to the voter, most likely,
when he looks back on many elections. Voting just by feel is of
course equally valid, and optimizes one's outcome too, if you haven't
estimated sincere ratings. Both approaches are valid. But if
you vote by feel, when it's different from what sincere ratings
& best Pij estimates say to do, then, after many elections, you'll
look back and regret that you let yourself be influenced by
risk-aversion, or whatever it was that made you vote-by-feel
votes differ from your sincere-ratings votes.

Summary: Both approaches are perfectly valid. The sincere-ratings
approach will look better to you whe you look back on many
elections. You'll have done better at maximizing how good the
outcomes have been, overall.

Mike Ossipoff





>Thus the
>'neural net' approach is probably the more accurate (although
>calculations involving ratings might help to get you into the ball
>park).

Who's to say which is more "accurate"? It seems to me that your
how-I-feel-like-voting estimate is based, intuitively, on
sincere ratings, estimated Pij, & how you feel about risk.
Of course, when voting by feel, none of those things are explicitly
estimated.

But it seems to me that if there's any difference in accuracy,
then it's more accurate to separately estimate each thing: The Ui,
the Pij (maybe estimate the Pij by estimating win probabilities, or
maybe calculate estimates from poll results).

I have nothing against the vote-by-feel way, and that's how I
myself have always voted. I've never written down Ui & Pij in
order to calculate how to vote in Plurality. So I'm not criticizing
the validity of vote-by-feel, but I'm only saying that the
method involving estimating the Ui & the Pij is perfectly valid too,
and is actually easier for me. The main reasons why I haven't done
that is because, for most elections, I hadn't heard of it, and
later because it was too obvious how to vote--no need to calculate
anything. That's a case where vote-by-feel is better. But there
will be elections where it _isn't_ obvious by feel, and your
vote-by-feel guess will feel more uncertain than your Ui estimates
and Pij calculations.


>
>So if, after calculating your intended strategy, you feel an urge to
>make a couple of changes, you would probably be right to follow your
>intuition.

Sure, if you feel more sure about vote-by-feel feelings, as I
usually do under actual U.S. voting conditions in nonmunicipal
elections. Sometimes vote-by-feel will feel less sure than
direct Ui estimates and Pij calculations based on win probability
estimates or poll results.

But if you look at your Ui & Pij strategy, and feel that you
want to do differently, then you're more sure of vote-by-feel
in that election. So you should change your vote to match how
you feel like voting.

Partly because maybe you're more confident in your vote-by-feel
instrumental strategy, and partly because maybe you don't feel
like voting instrumentally.

Mike Ossipoff




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