[EM] Strategy question

[Raph Frank]

On Tue, Sep 8, 2009 at 3:18 PM, Kristofer
Munsterhjelm<km-elmet at broadpark.no> wrote:
> Which one is preferrable? One might, in a way, say that the two are
> equivalent. If your preferences are
>
> A > B > C > D
>
> and the poll is
>
> 100: C
> 98: B
> 90: D
> 20: A,
>
> then voting {A, B} is an offensive strategy from the point of view of A (you
> vote B to increase the force against C), but a defensive strategy from the
> point of view of B (you vote for A so your vote of B won't hurt A). The only
> real difference is which is the "least of two evils" - since B is, B's point
> of view is the true one, and this is a defensive strategy.

You need to give info on utility too to determine optimal strategy.

You can go through each tie in order of probability.

Tie 1: C,B

You should vote for B.

Tie 2: C.D

You should vote for C.  However, voting for C weakens your vote in tie
1, so it is better not to vote for C (as tie 1 is much more likely
than tie 2).

Tie 3: B,D

Your vote for B is correct for this one, so no change.

Tie 4: C,A

You should vote A

Tie 5: B,A

This is slightly less likely than C,A.  Your vote for A is more likely
to cause A to beat C than A to beat B.

The rest of the tied don't matter.

The best vote is likely B+A.

The rule could be something like

"vote for the best of the top-2 and the highest polled candidate who
you prefer to the expected winner".

It is highly likely that the vote between the top-2 will be the only
one that matters, so the vote is reasonably optimal.  The 2nd vote
falls into the tie 4 vs tie 5 category.