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

[MIKE OSSIPOFF]

>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.

You use the word "proof" in quotes, as if I'd used the word. I
didn't use the word "proof". I said "demonstration". But you're
right. My demonstration didn't take into acount 3-way ties.

I call attention to the fact that you told me that right after I
told it to you. Yesterday I posted that I'd been unjustifiably
assuming that all ties were 2=way ties. So now, after I say that,
you're pointing it out to me.

So my demonstration that, with any number of candidates, very few
voters, & 0-info, the above-mean strategy maximizes expectation isn't
a valid demonstration. It contains an unjustified assumption, as
you pointed out after I told it to you.


> > 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.

My argument that my vote for j doesn't affect Pij depended on
my unjustified assumption that ties are 2-way, the unjustified
assumption that I told you about yesterday.

With n-way ties, the the probability that my vote for i will change
the winner from j to i can depend on whether or not I voted for j.
That's why I told you yesterday that I no longer claim to have a
demostration that above-mean strategy always maximizes expectation
when there are very few votes.







If you don't believe it [...]

I believe it. That's why I told you about it yesterday.

>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?

One difference is that his vote is covered by Pij, as I defined it.

But whether or not I find your reason convincving, there are other
reasons why I now realize that Pij can be affected, when there are
very few voters, by whether or not I vote for j, when Pij is defined
as the probability that my vote for i changes the winner from j to i.

But I told you yesterday that I no longer claim that I have a demonstation 
that 0-info expectation maximizing strategy with very
few voters is the above-mean strategy. So I'd say that you're a
little late in refuting that claim, since I posted yesterday that
I've abandoned that claim.

It may well be that 0-info expectation maximizing strategy is still
the above-mean strategy, even with very few voters. But I said
yesterday that I no longer claim to have a demonstration of that.

Mike Ossipoff


>
>  -- Richard
>
>

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