On Sun, Mar 28, 1999 at 01:12:34AM +0000, Nick Bostrom wrote:
> Wei Dai wrote:
> > 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.
Several people have answered my first question with "yes", and an implicit assumption in their reasoning is that before you know what your number is you should reason as if the 100!-th digit of PI is uniformly distributed. This assumption, along with the Self-Sampling Assumption is needed to reach the above conclusion. But of course the 100!-th digit of PI has a definite value and is not random. So how do we justify the use of the uniform distribution here? And in general when faced with a computational problem that we can't solve, (1) does it always make sense to reason as if there is a probability distribution on the answer and (2) how do we come up with this distribution?