[EM] Approval strategy A

[Rob LeGrand]

I wrote:
> Strategy A: Approve all candidates I prefer to the current CRAB
> first-placer; also approve the first-placer if I prefer him to the
> second-placer.
>
> [S]trategy A always homes in on the Condorcet winner when one exists
> and all voters use the same strategy.

My 25-candidate simluations still haven't found a single contradiction to the
above statement after over 15000 elections, but I've been able to engineer one
with four candidates.  If the voters have the preferences

50:A>B>C>D
26:A>C>D>B
25:C>D>B>A
50:D>B>C>A

it's possible for CRAB to get stuck in the cycle B->C->D->B even when all
voters use strategy A.  Candidate A beats them all pairwise but only barely,
and if A doesn't start out in first place he might not get there.  But if he
did, he'd stay in first.  When all voters use strategy A and a stable winner
emerges, it's always the Condorcet winner.  Otherwise, there's a cycle of
frontrunners.  Generally, the candidate who defeats the current leader by the
largest margin becomes the next leader.  It's my opinion that strategy A does
as well as possible when the only available information is the current approval
percentage of each candidate.  And when most of the other voters use strategy
A, so far it seems to be overwhelmingly in your best interest to use it too,
making strategy A something like an evolutionarily stable strategy (see
Evolution and the Theory of Games by John Maynard Smith or The Selfish Gene by
Richard Dawkins).  I'm working on simluations to show the general truth of that
conjecture.

Here's my philosophical argument for using strategy A when you only know
current approval of each candidate.  In the absence of a reliable way to
estimate each candidate's odds of winning, it seems reasonable to assume that
the current poll leader is very likely to win (so his utility for you is your
best estimate of the expected outcome's utility for you), and the second placer
is the most likely to catch up to him.  When deciding which pairs of candidates
are most important to bring your vote to bear on, it makes sense to rank them
1st/2nd, 1st/3rd, 1st/4th, etc.  So you should always vote for your favorite of
the top two and not for the other.  Then you should vote for the third-placer
if he's better for you than the first-placer, and so on.  That's the way I
think of it, anyway.

--
Rob LeGrand
honky98 at aggies.org
http://www.aggies.org/honky98/

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