[EM] Approval Strategy

[MIKE OSSIPOFF]

It's true that no Approval strategy formula is useful for everyone, or even 
every progressive.

Certainly I disagree with most progressives' Plurality strategy, which I 
claim is based on unreliable information. But even if it were true that 
Kerry were the best that we could get, I still wouldn't have voted for him, 
in Plurailty or Approval, because he didn't deserve a vote.

So when I discuss Approval strategies, I describe a number of them.

Best Frontrunner strategy:

The strategy that James was improved on by someone who said: Vote for the 
candidate that you'd vote for if it were Pluralty, and for everyone whom you 
like better.

That would be my general advice for Approval voting.

Maybe that could be called the Plurality & Better strategy. I'm capitalizing 
the names of the strategies for clarity.

If somone wanted that worded from scratch, I'd call it the Best Frontrunner 
strategy, and word it thusly:

Of the 2 candidates whom you expect to be the top 2 votegetters, vote for 
whicheve of those you prefer, and for everyone whom you like better.

Enhanced Best Frontrunner:

I've discussed an enhancement of Best Frontrunner that considersd those 2 
candidates' probabilities of outpolling eachother, and the other candidate's 
probability of being in a tie or near-tie with the higher of those 2 
votegetters.

Say F1 & F2 are the 2 whom you expect to be the frontrunners.

You prefer F1 to F2, so you vote for F1, and not for F2. But do you vote for 
some other candidate X too? Of course, if he's better than F1. And of course 
not if he's worse than F2. But maybe if he's inbetween.

The only time when it matters whether or not we vote for X is if he's in a 
tie or near-tie for 1st place. What I mean by saying that X is tied or 
near-tied with Y is that if you vote for X and not for Y, you make or break 
a tie for 1st place between X & Y.

So the question of voting for X only matters if he ties or near-ties 
someone. For this level of enhancement, assume that that someone has to be 
F1 or F2.

Say P1 is the probability that F1 outpolls F2, and P2 is the probability 
that F2 outpolls F1.

Vote for X if:

P1(U1-Ux) < P2(Ux-U2)

The expectation of harm for voting for X, if it does harm, is less than the 
expected gain from voting for X, if it does good.

Re-arranging,

P1U1 - P1Ux < P2Ux - P2U2

Ux(P2+P1) > P1V1 + P2V2

P2+P1 = 1, so:

Ux > P1V1 + P2V2

If F1 & F2 are equally likely to outpoll eachother, or if there's no 
information available about that, which amounts to the same thing, then:

Ux > (P1 + P2)/2

...which is the same strategy that someone has described here. Vote for 
everyone who is better than the mean of F1 & F2.

Another thing that can be said about this is that it's the same as saying to 
vote for X if he's better than the election's expectation--since it's 
assumed to be virtually assure thing that either F1 or F2 will win.

If so, then why do we even bother to vote for anyone else, such as those 
whom we prefer to F1, or those who are better than (F1+Ff2)/2? Just on the 
chance that maybe it isn't really quite 100% that no one will tie or 
near-tie F1 or F2.

>From the paragraph before last, under these assumptions, this enhanced Best 
Frontrunners strategy is also the Better than Expectation strategy.

Better than Expectation Strategy:

Vote for each candidate who is so good that you'd rather have him/her in 
office than hold the election.

That's the same as saying to vote for everyone who is better than your 
expectation in the election.

When there is 0-info, this is the same as the 0-info strategy of voting for 
the above-mean candidates.

It's been shown that, by some reasonable approximations, Better Than 
Expectation maximizes your expectation.

It's a matter of which facts are most obvious to you. Do you have a strong 
sense that a certain 2 will be the top votegetters? If so, then Best 
Frontrunner is good. If not, then Better Than Expectation is likely better.

Formulas Are Usually Not Needed:

But I'm getting ahead of myself, because I don't usually start with these. I 
usually say point out that
one usually knows how one wants to vote, and all this talk of strategic 
dilemmas is mostly academic. But if you don't know whom you want to vote 
for, the forumlas can help.

Why not just vote for everyone who deserves a vote?

Completely Unacceptable Candidates:

If the winnable candidates are in 2 sets such that the merit difference 
within those 2 sets is negligible compared to the merit difference between 
those wets, then vote for the better-set candidates, and not for the others.

For instance, if you agree with me that there are completely unacceptable 
candidates who could win, then vote only for all the acceptable candidates.

But be particular about whom you consider acceptable, ok? We really can do 
better than electing a crook, a liar, or a sleaze.

Mike Ossipoff

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