[EM] Approval strategy answer

[MIKE OSSIPOFF]

>
>I'll announce the approval/cumulative voting strategy that I think is
>useful for voters with little information about other voters. There are n
>candidates. Vote for the n/2 or n/2 + 1 candidates you most prefer.
>
>Any other suggestions?

Your suggestion maximizes utility expectation when there
is no information about frontrunner probabilities, and also
no cardinal utility estimates--instead of estimating the
candidates' utility you've only ranked them. In that case,
it's as you suggest: Your best strategy is to vote for the
best half of the candidates.

But that isn't realistic. Surely if you can rank the candidates
in order of merit, you can assign a number rating to their
merit. The ranking doesn't reflect all you know about how good
the candidates are. When you have utility estimates rather than
just a ranking, but you still have no frontrunner information,
then you maximize utility by voting for all the candidates who
are above average in utility.

But, at least in public political elections we always have
an idea of winnability & frontrunner probabilities, doen't we?
After all, FPTP voters use it all the time, and discuss their
use of it for their strategy. The lesser-of-2-evils strategy
so popular in FPTP can be explained in terms of Plurality's
strategy that makes use of utilities and frontrunner probabilities.

***

What is that strategy, for FPTP & Approval, when you have
utility estimates & frontrunner probabilities?

First let me define "strategic value":

Preliminary definitions:

Pij is the probability that i & j will be the 2 frontrunners.
Ui is i's utility.

i's strategic value is:

The sum, over all j, of Pij(Ui-Uj).

***

In Plurality (FPTP), vote for the candidate with the highest
strategic value.

In Approval, vote for all the candidates with positive
strategic value.

***

But it isn't necessary to talk about the mathematical strategy
when proposing Approval. It wouldn't be fair, because Plurality
has mathematical strategy very similar to that of Approval.
People know how to vote in Plurality without (explicitly) using
mathematical strategy, and they can vote in Approval just as
easily. Just tell them to vote for the candidate whom they'd
vote for in Plurality, and also for everyone whom they like
more.

I believe that voters' judgement of whom to vote for is based
on estimates of the mathematical strategy, even though voters
don't say it that way.

***

Mike Ossipoff

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