[EM] Richard's Approval strategy

[MIKE OSSIPOFF]

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.

You mean in addition to the time that you wasted by making that
incorrect statement and thereby starting the issue?

Look, you agreed that Bart's quotation is about a probability that's
defined only when there's a tie for 1st place. If you don't agree with
that, you could take another look at Bart's wording. You said that
you agreed that the "given" clause isn't part of the "that" clause
and that the probability is defined only if there's a tie for 1st place.

So when that probability is defined, which means when there's a tie
for 1st place, i & j are the candidates in the tie if & only if they're
the ones with the highest vote totals.

When I showed that Bart's wording was about a probability that's defined 
only if there's a tie for 1st place, you then said that
that's what you said all along. But since we (now) agree that Bart's
wording says that, maybe now you've forgotten that you've accepted that
literal interpretation of Bart's words. And so you're back to repeating
that, under the conditions under which Bart's probability is defined,
it's the same as the probability that i & j are the 2 frontrunners.

Whether you reply to this or not doesn't matter. Whether you do or not,
it's obvious to everyone else that you were & are mistaken to say
that Bart's probability, under the conditions under which it's defined,
can be different from the probability that i & j are the 2 highest
votegetters.

>
> > >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?

The _Discover_ article said that Approval was used in Venice in the
late middle ages or soon after. I don't know if it was _exactly_
Approval. If so, then Weber re-invented it.

Weber had an article in _Journal of Economic Perspective_ for Winter '95.
If that isn't the right year, I hope Bart will correct it.

>
> > 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.

Richard, it's been known where the strategy comes from ever since
Weber demonstrated it several decades ago.

>
> > 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

Yes, and that's what I was asking for, along with a method for getting
your increments & decrements from it, and with a numerical example.

>, not on the specific numerical data.

But you could add those too, if the method is workable.


>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.

Yes, and that's why I asked you to name a "type of intelligence" that
can be gathered or reasonably estimated, and which can be used to get
your increments & decrements.

>
> > 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, in other words, you method might be no good unless there are
very many voters.

If your method differs in its results from Weber's method, which has
been amply demonstrated to maximize utility expectation, then your
method doesn't accomplish that. Maybe you're saying that it comes close
enough for practical purposes when there are very many voters, but
what good is a method that isn't as accurate, when there's been one
that's more accurate--a method that's been well known for some decades?




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

How? And what would be the advantage of doing that instead of just
using Weber's method? Especially since you doubt the accuracy of your
method?

>
>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.

So far you haven't shown how your increments & decrements can be
gotten at all--easily or difficultly. And if your of-theoretical-interest
method is less usable, then no doubt you won't be offering it as
a way to actually determine Approval strategy.

Mike Ossipoff


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