Re: probability and decision theory

From: Wei Dai <weidai.domain.name.hidden>
Date: Tue, 17 Mar 1998 01:21:27 -0800

On Mon, Mar 16, 1998 at 07:47:22AM -0800, Hal Finney wrote:
> Mathematically, probability is defined as a measure applied to the set of
> subsets of some base set. Each subset has a measure, which is a number
> that must satisfy the property that measure of the union of two disjoint
> subsets is the sum of the measure of the two subsets. If the measure of
> the universal subset is 1, then this is considered a probability measure.

I guess what I'm saying is that in trying to solve the paradoxes we can't
just look at probability theory. Instead we should look at decision
theory, and try to come up with one that is compatible with AUH. The new
decision theory may not even have to do with the traditional concepts of
probability.

(I take back my earlier suggestion that we fix probability theory first
and then worry about decision theory. That doesn't work because
probability theory by itself is just a mathematical structure. It is
decision theory that makes use of probability theory and connects it with
the real world.)

> I think you can still look at evolution and see what kinds of
> decision theory and probability theory will evolve. We know that we
> are replicators and have developed our instinctive understanding of
> probability over a long period of time. This should be able to be
> analyzed and understood. You might be able to create a toy universe
> of evolving replicators and see what kinds of probability theories are
> most useful and successful.
>
> The fact that we may apply probabilistic reasoning in understanding
> evolution does not seem circular or paradoxical to me. Probability and
> logic are tools which are applied successfully in a wide range of areas.
> It may be that in some of our discussions we are extending them into areas
> where they don't work so well (like your copying paradoxes). But that
> does not mean that they are useless in general. Sticking to well defined
> and explored areas, like evaluating the behavior of evolutionary systems,
> we can confidently use probability theory, logic, and other tools to
> develop our theories and understanding.

Yes, but you can't use probability theory to decide which decision theory
to accept as a normative theory, because by using probabilities you've
already accepted a normative decision theory.

> I don't really understand this. Assuming that we are like other people,
> and if we have a theory that tells us how we should act, and we actually
> follow the theory, then this same theory should tell how other people do
> act. Maybe I'm missing the point here.

I agree that normative and positive decision theories will tend to be
similar. The point is that they serve different roles, and are judged on
different bases.
Received on Tue Mar 17 1998 - 01:21:57 PST