reasoning under computational limitations

Wei Dai (
Sat, 27 Mar 1999 16:36:59 -0800

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 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.