[EM] More 0-info pairwise strategy

[MIKE OSSIPOFF]

David Catchpole said:

>On Wed, 29 Mar 2000, Markus Schulze wrote:
>
> > Suppose that p(B,A) is the calculated probability that
> > you change the winner from candidate B to candidate A
> > when you vote A > B > C > D sincerely. Suppose that
> > p(B,C) is the calculated probability that you change
> > the winner from candidate B to candidate C when you
> > vote A > B > C > D sincerely. Suppose that u(X) is your
> > von Neumann-Morgenstern utility of candidate X. Then:
> > If p(B,A)*(u(A)-u(B)) < p(B,C)*(u(B)-u(C)), it is
> > advantageous for you to vote A = B > C > D insincerely
> > instead of A > B > C > D sincerely.
>
>...this implies non-zero information. Can I just say that our
If we know those 2 probabilities, in some way other than getting
them by assuming that every possibility is equally likely, then
of course that isn't 0-info. But even if we don't have any
information, we can still have those probabilities, based on
how may of the equally-probable situations will make each of
those things happen. So 0-info doesn't mean no probabilities can
be determined. Calculating utility expectations depends on
having probabilities, and we can have those with 0-info if we
get them by counting how many of the equally probable situations
will have each of those 2 effects. If you take a card from a deck,
I have no information about what card you drew, but I can still
tell you the probability that you drew the Ace of Spades: 1/52.

discussions
>of "black-box" strategy are really freaking me out? This is some weird
>philosophical **** going down.

The 2 probabilities that Markus named aren't known other than by
calculating them from pure chance, on the assumption that all
pairwise-defeat configurations are equally likely, and, within
each defeat configuration, all choices of which defeat is the
one that we could reverse are equally likely too.
And all pairs of pairwise defeats in that configuration are equally
likely to be the pair of defeats that are so close that we could
reverse their magnitude comparisons (margins or wv).

Tell me your utilities of the candidates, and, with lots of
computation, I could tell you those 2 probabilities in a margins
election, based on 0-info, with no situation being more likely
than any other situation. I'd count how many situations there are,
and how many would have each of those 2 effects.

>
>It seems we must always have some kind of information or assumptions about
>the "black-box" situation to which we are responding- in other words, it
>is not possible to have a zero-information situation.

The only information used in these 0-info strategy determinations
is the realization that we don't know of any reason why any
situation should be more likely than any other, so, from our
point of view, they're all equally likely.

So, in that sense, there's no "zero information", since the
information that we don't know which situations are more likely
than other situations is itself a piece of information. What
we mean, then, by 0-info, is that that's the only information we
have. That one piece of information is enough to give us those
2 probabilities that Markus mentioned, and is enough to
calculate strategies to maximize utility expectation.

Mike Ossipoff



>
> >
> > Markus Schulze
> > schulze at sol.physik.tu-berlin.de
> > schulze at math.tu-berlin.de
> > markusschulze at planet-interkom.de
> >
> >
>
>--------------------------------------------------------------------
>Politeness be sugared, politeness be hanged,
>Politeness be jumbled and tumbled and banged.
>It's simply a matter of putting on pace,
>Politeness has nothing to do with the case.
>						Norman Lindsay
>						"The Magic Pudding"
>

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