Re: Decision theory

From: Wei Dai <weidai.domain.name.hidden>
Date: Tue, 5 Jan 1999 17:15:41 -0800

On Sun, Jan 03, 1999 at 07:32:09PM -0500, Jacques M Mallah wrote:
> On Sun, 3 Jan 1999, Wei Dai wrote:
> > 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?
>
> Wrong. It is not true that no matter what I decide, I will have
> the same utility. What is true is that only one decision is possible in
> this particular case. I just don't know which one yet.

Why is it wrong? Didn't you say earlier that in a theory with no free
parameters all possible courses of action must occur? Why do you now
say only one decision is possible? I'm having a lot of
trouble understanding this reply.

> I'll say it again: my mental processes *are* the laws of physics
> in action, and *do* have consequences. My choice *does determine* the
> actual utility, which is to say, the laws of physics determine it.
> I can't overemphasize the above point. Stop and think about it
> if you feel tempted to just keep reading.
> Forget I said anything about subsystems. I'm sorry; I was wrong
> to have done so. Utility functions are defined over any hypothesized
> state of the universe. It is redundant to say it is defined over a global
> state: that is true by definition.
> In general, they only depend on the (unnormalized) measure
> distribution of consciousness, since why should I care about anything
> else? Any hypothesized situation where I can calculate how many
> computations of each type would be implemented should give me the utility
> function for that situation.

I'm with you so far.

> Even if a hypothesis is not truly self consistent, an
> approximation to that hypothesis can be, and is the best I can do. Since
> we know I won't be able to show which decisions are unphysical a priori,
> my most accurate approximate calculated utility for that hypothesis is a
> well defined quantity. It is however a function of who I am.
> It is also true that, assuming I pick the choice with the highest
> utility, and that my calculations are correct, that the actual utility
> will be that highest value.
> So another way to look at it is that to calculate the actual
> utility, I have to also calculate a bunch of other values as an
> intermediate step. Then I should decide to do what I've just shown that
> the laws of physics make me do under those assumptions.

Now I'm lost. I have no idea what the above three paragraphs mean.

> I'm not sure how to define it in a language-independent way. It
> probably can't be done, which would pretty much guarantee the truth of
> my belief that it can't have a well defined value that is equal to zero.

Now that I think about, it doesn't make sense to have a theory with zero
information content. It should be the universe that has zero information
content. The theory should define what information content means, and then
simply state that the actual universe is the unique universe that has zero
information content.
Received on Tue Jan 05 1999 - 17:19:26 PST