[EM] Richard's Approval strategy

[Richard Moore]

MIKE OSSIPOFF wrote:

> >I think it's time to move off this lengthy digression.
>
> Yes, because I think now we both understand that my Pij definition
> and the one that Bart posted are just different wordings of the
> same definition, and that they both define the same probability.

For the record, I disagree with that, but I'm not going to waste any more
time on it.

> >The original topic
> >of strategy is what we should be discussing.
>
> Yes. Your ZI Approval strategy is equivalent to just voting for
> the above-the-mean candidates, a strategy that's been well-known
> ever since Weber invented Approval in the '70s.

Approval invented in the '70s? I thought I'd read that it's been used
for centuries. Maybe he was the first modern advocate for approval
voting or did the first mathematical treatment of it. I really don't know
anything about Weber. Any more information on this?

> Also, of course
> there's no point in doing your ZI calculations when one need only
> vote for all the above-mean candidates.

There isn't a need, for practical applications, but from a pure
theoretical
standpoint it's nice to understand where that strategy comes from.

> As for your non-ZI strategy, I asked you how you'd get the probability
> differences that it uses--the amount that you increase
> i's chance by voting for i, and the amounts by which you decrease
> each of the other candidate's chance by voting for i.
>
> Your answer was that it depends on what information is available
> to you. I think we all knew that.

I actually went farther than that. I said it depends on the TYPE of
information, not on the specific numerical data. The method should
accommodate any type of information that can be translated into
outcome probabilities. But doing that translation is outside the scope
of the method itself; it is specific to the type of intelligence that is
gathered.

> What I'd asked you for was
> some kind of available or plausibly-estimated figures of some kind,
> and your demonstration of how you'd use those to get the probability
> increments & decrements that your method uses.
>
> So what would be an example of a type of available or plausibly
> estimated information about the election, and your method for
> determining your win-probability increments & decrements from it?
>
> I'm just trying to find out if you can use your method.

I'll have something to post on this in a few days. I went through the math

and found, as I suspected, that it's the same as Weber's method. Well,
it's either the same, or only differing by a small error term which should

be negligible for large populations. So if you can calculate Weber's
probabilities, you can apply a slight transformation to get the ones I
described. Or vice versa.

I'm not nearly as interested in the application of the non-ZI method as
I am in the theory of it, so whether those calculations can be performed
easily doesn't concern me.

 -- Richard