[EM] How to vote in Approval

[MIKE OSSIPOFF]

Demorep wrote:

Mr. Ketchum wrote in part-

Trying to be simple can be deceptive. Approval is easy to count,
and sounds easy to vote until you have a ballot in your hands with a list
of 4 lemons and need to decide how many of them you want to call "approved".
---
D- Approve NONE so that NONE get elected.

I reply:

Yes, don't vote for lemons. If some lemons are sourer than others,
they're still all sour. A lesser-evil is still an evil.

I claim that, in our public political elections, there are always
unacceptable but winnable candidates, and under those conditions,
one's best Approval strategy is to vote for all of the acceptable
candidates, and not for any of the unacceptable candidates.

Under those conditions in a Plurality election, vote for whichever
acceptable candidate is most likely to be able to be helped by you
to prevent an unacceptable candidate from winning.

Note how much simpler it is in Approval.

What if all the candidates are unacceptable? Don't vote for any
of them. The pitifully minimal gain from voting for the less
disgusting one(s) isn't worth it. Don't validate that "choice" by
voting among those candidates.

If there are no absolutely unacceptable candidates, then strategy
isn't so simple. But, if we have some sort of winnability information,
as we do in our political elections, then if you'd vote for a lesser-
evil in Plurality, vote for him in Approval too, but also vote for
everyone whom you like better, including your favorite.

Of course if there are unacceptable candidates, but they aren't winnable, 
then the above paragraph applies there too.

What follows is for elections where there are no winnable unacceptable
candidates:

If there's no winnability information, that's called a 0-info
election, and your best Approval strategy in public elections is
to vote for all the candidates whose merit for you is above the
mean.

By the way, mathematical strategy has been discussed for when
there's winnability information ("probability-info"):

Preliminary definitions:

Ui is the utility (worth) to you of candidate i.

Pij is the probability that, if there's a tie for 1st place, it
will be between i & j.

The strategic value of candidate i is:

The sum, over all j (j not equal to i) of Pij(Ui-Uj)

In Approval, vote for all the candidates whose strategic value is
greater than zero. In Plurality, vote for the candidate with highest
strategic value.

Someone pointed out that it's a fair approximation, when one doesn't
have more accurate information, to say that Pij is proportional to
the square root of the product of i's probability of winning and
j's probability of winning. As an approximation one could say that
the probability that i will be in a tie for 1st place if there is
one is proportional to the square root of i's probability of winning.
For Pij, multiply those tie-probabilities of i & j.

The purpose of that is that it might be easier to estimate the
candidates' probabilities of winning than it is to estimate the
probability that i & j will be in a tie for 1st place if there is one.

Derivation of that approximate way of estimating can be found
at http://www.barnsdle.demon.co.uk/vote/sing  at the Approval strategy
page. In fact the other Approval strategy statements that I've made
here are justified at that website. It needs to be updated. For instance,
I sometimes used "frontrunner probability" interchangeably with
"tie probability", and I haven't corrected that error at that website
yet.

Mike Ossipoff


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