> Suppose you wake up in a universe which contains a total of 20 people. Ten
> of them have been assigned numbers 0 to 9, and the other ten have been
> assigned the number equal to the 100!-th digit in the decimal expansion of
> PI. You are told your number but not anyone else's, and you are
> asked to guess the 100!-th digit of PI. Assuming that you can't actually
> compute that digit, it seems intuitive that your best guess would be your
> own number.
>
> My questions are (1) is this correct
I would say Yes. It follows from the Self-Sampling Assumption, which (crudely put) states that you should reason as if you were randomly sampled from the set of all observers.
> and (2) are there principles of
> reasoning under computational limitations (perhaps extensions of
> probability theory?) that can be used to derive or justify this and
> similar conclusions? Any relevant references would be appreciated.
Reasoning under computational limitations is a very underdeveloped field. In any case I don't think much of that would be applicable here. What is relevant is rather the literature about the Doomsday argument and the anthropic principle (which you of course already know a lot about). Check out my web site at http://www.anthropic-principle.com.
Nick Bostrom
http://www.hedweb.com/nickb n.bostrom@lse.ac.uk
Department of Philosophy, Logic and Scientific Method
London School of Economics