From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Sat Mar 27 1999 - 18:22:41 MST
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
Yes.
> (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.
Of course. There are eleven people with the correct digit and nine
people with nine different incorrect digits. Ergo, your digit is
probably the right one.
Furthermore, even if there were only four people and only one had the
correct digit, it would still be correct to guess your own digit instead
of picking a random different digit. That way your chance is one in
four, while otherwise your chance is one in twelve - the probability you
do not have the correct number already (3/4) times the probability of
choosing the correct digit (1/9).
--
sentience@pobox.com Eliezer S. Yudkowsky
http://pobox.com/~sentience/AI_design.temp.html
http://pobox.com/~sentience/singul_arity.html
Disclaimer: Unless otherwise specified, I'm not telling you
everything I think I know.
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