[EM] 3 candidates, few voters, 0-info

[Richard Moore]

MIKE OSSIPOFF wrote:

> Richard wrote:
>
> >MIKE OSSIPOFF wrote:
> >
> > > It seems to me that the above-the-mean strategy is still valid
> > > no matter how few voters there are, as long as there are only
> > > 3 candidates.
> >
> >Then can you explain the following? I posted this at the end of my
> >previous message:
> >
> >"If we replace voters 1, 2, and 3 with three groups of 1000 voters
> >each, with the preferences and voting probabilities indicated in the
> >example, then I think the mean utility strategy would work (because
> >of the equal probabilities) even though it is not a true ZI case."
>
> I can't explain it because I don't believe that it's so. Write the
> example. Show that your expectation is better if you vote for A & B
> than it would be if you voted only for A.
>
> But you needn't, because I've shown that, even with very few voters,
> 0-info strategy is to vote for the above-mean candidates.

Mike,

I don't think your "proof" included 3-way ties and other close 3-way
scenarios so I'm not convinced its valid. Maybe you should fully
calculate all the probabilities for 3 candidates, 3 voters other than
yourself, and zero info about the other voters' preferences, and
see how it works out.

> >As the population shrinks, won't the Pij start to diverge (because of
> >the effect of your certain A vote),
>
> No, because Pij has nothing to do with your vote. Pij is about how
> _other people_ vote. Pij is about a certain tie or near-tie existing
> before you vote.

It's true that Pij is not affected by the vote you are evaluating, but
a vote you've already cast does affect Pij. If you don't believe it
does, consider this scenario: Suppose for some reason you (and
you only) are barred from voting for A, so you just want to decide
between a B vote or no vote at all. Now suppose there is a fifth
voter, and you have found out there is a 100% certainty that the
fifth voter will vote for A. The other three voters remain as in the
original example. If "Pij is about how _other people_ vote", then
you would factor in the information about the fifth voter. But
statistically (and therefore strategically), you cannot distinguish
between this case and the original example, where there is no
fifth voter but you are assured of your own A vote, can you?

 -- Richard