Re: a baysian solution

From: Wei Dai <weidai.domain.name.hidden>
Date: Tue, 14 Apr 1998 16:30:27 -0700

On Wed, Apr 15, 1998 at 12:00:48AM +0000, Nick Bostrom wrote:
> So far so good. But what if we replace "M" with "The guy whose name
> is Nick Bostrom." Now, without knowing anybody's rank, I can ask the
> question: "What is the probability that the guy whose name is Nick
> Bostrom has a rank less than or equal to 100?" And we can ask: "What
> is the probability that there the real universe is B, given that the
> guy whose name is Nick Bostrom turns out to have a rank of 74?" There
> seem to be well-posed questions, and they seem to suffice to produce
> the Doomsday argument. For suppose I suffer from amnesia and can't
> remember anything about my birth rank. Based on other considerations,
> I assign a fifty-fifty probability that the universe is A/B. I can
> then, in this situation, ask: "What's the probability that the guy
> who's called Nick Bostrom should have a rank less than or equal to
> 100, given that the universe is B?" Since I don't have any other
> relevant information, by the principle of indifference I should
> answer: "1/2". The same question for universe B get the answer: "1".
> When I then discover that the guy called Nick Bostrom has birth rank
> #74, I have to make a probability shift. The Doomsday conclusion
> follows from this.

P(Rank(Nick) <= 100 | universe B is real) is either 0 or 1, depending on
what universe B is. You can ask about computational limitations, but I
think we need to assume no computational limitations at this point. I have
not heard of any systematic way to integrate computational costs into
decision theory, and this project is way to big for us to tackle here.
(Although if you can prove me wrong I'll be very happy!)
Received on Tue Apr 14 1998 - 16:31:16 PDT