Re: Decision theory

From: Wei Dai <weidai.domain.name.hidden>
Date: Sun, 3 Jan 1999 15:05:53 -0800

On Sun, Jan 03, 1999 at 04:40:19PM -0500, Jacques M Mallah wrote:
> No, I do not see a problem.
> In the usual case, to make a decision I consider different
> scenarios, which I can model using a physical theory and treating the
> decision to be made as a free parameter.
> Even if I believe in a theory with no free parameters, there will
> never be any reason I can't use that algorithm.
> The only difference is that the scenarios not chosen are
> unphysical for a different reason than before: due to the laws and not
> just the actual parameters. Despite that, no matter how much physics I
> know or how much calculation I do, there is no danger that I can tell a
> priori which ones are inconsistent until I make the decision.
> This means that I must be using approximations, but that is also
> guaranteed to be so even in a theory with free parameters.

But there is no provision in Baysianism for dealing with computational
limitations and approximations... unless there is and I just don't know
about it? But that's really a side issue...

Doesn't it strike you as silly to say "I know whatever I do, I'll have the
same actual utility, but I'll do this because when I plug this into my
approximation algorithm, it gives the me the highest approximate utility."

If my utility function is defined over global states of the universe and I
believe in a theory with no free parameters, then I know (can prove) that
no matter what I decide, I will have the same utility, even if I can't
compute what that utility is. Therefore utility functions can't be defined
over global states of the universe, but what should they be defined over?

> As I explained before, I don't see how a theory that includes 'all
> possible structures' can have no free parameters.
> One reason theories with no free parameters are of interest is
> that quantum gravity may turn out to be such a theory. It would however
> be strange if other mathematical structures don't also exist.
> In part, the definition of a free parameter is arbritrary. Any
> theory can be viewed as a special case of some set of theories. The
> important thing is really the information content of a theory, and I don't
> think it can be zero.
> As for your proposal, from what I recall of it - and you may want
> to redescribe it under a seperate thread subject - it did not seem that
> plausible to me, possibly because I did not get the impression that it
> dealt with programs actually being implemented instead of just sitting
> there.

How do you define the information content of a theory? It seems every
theory must have a non-empty shortest description, unless there is a
theory that all sufficiently intelligent beings think is obvious and
obviously true, and therefore doesn't need to be described. If that's the
case, what a cruel joke to all those theoreticians writing papers all day
long.
Received on Sun Jan 03 1999 - 15:09:45 PST