Re: Decision theory

From: Jacques M Mallah <jqm1584.domain.name.hidden>
Date: Sat, 9 Jan 1999 21:53:31 -0500

On Sat, 9 Jan 1999, Wei Dai wrote:
> On Wed, Jan 06, 1999 at 02:05:20PM -0500, Jacques M Mallah wrote:
> > To say that I affect the outcome is to say that my mental
> > processes, or computation, determines the result, which is still true.
> > And the utility function, for my decision making, must be calculated by me
> > with different scenarios for each possible decision-outcome, because I do
> > not know what my own computation is.
>
> Ok, I think I understand what you're saying now. But of course you have to
> use an approximation instead of the actual theory to do this calculation.
> So the question is what approximation do you use, or more fundamentally
> how do you tell whether an approximation is a good one? The major problem
> I see is that the approximation has to handle counter-factual scenarios.
> What is to prevent it from giving arbitrary predictions in those
> scenarios, since you can't compare those predictions with the actual
> theory?

A major constraint is that, with the finite amount of calculation
that you do, even if you know the correct physics in principle, you would
not be able to show a priori that any of the scenarios is counterfactual.
Each scenario is supposed to represent your best estimate of what
would happen. Of course in practice your estimates would be much cruder
than the limits imposed by Godel's theorem. The only way you could get
arbritrary predictions is if you were arbritrarily stupid.
For example, if you know energy is conserved, then none of your
scenarios would be shown in your analysis to violate that constraint.
Is is possible that, in a chaotic system, your estimates would
become very bad for large time - but there's no way to avoid that, you can
only try to improve your estimates so far. It's known as the law of
unintended consequences - any decision you make is bound to have some.
Since you don't know what they are, you can't really take them into
account, except in a general way by planning for an iterative series of
decisions. The consequences of many decisions can be divided into a short
term component, which you can model well, plus a long term component which
you can treat as random and ignore when comparing your estimated utilities.
But all this practical stuff is far removed from physics by this
point. The interesting thing is the universality, that there is no way to
escape from such considerations even in principle, regardless of the laws
of physics.

> > Would such a theory be unique? If so, and I doubt it but would
> > like it to be true, it would make sense to speak of information content as
> > a well defined quantity.
> > Then we would have a mathematical theory of information content,
> > as well a theory of physics. The theory of physics, however, would have
> > zero information content, as defined by the other theory.
>
> See the new thread I started with subject "information content of
> measures."

I would need more time (and probably a look at that book you
mentioned) before commenting on it.

- - - - - - -
Jacques Mallah (jqm1584.domain.name.hidden)