Re: a baysian solution

From: Wei Dai <weidai.domain.name.hidden>
Date: Fri, 17 Apr 1998 10:42:15 -0700

On Thu, Apr 16, 1998 at 08:23:33PM +0000, Nick Bostrom wrote:
> But A and B can stand for *classes* of possible universes. In every
> univese of class A, the coin landed heads (say), and in every
> universe of type B, the coin landed tail. Each of these possible
> universes contains a person called Nick. Suppose I know that exactly
> one of these universes is the real one, and that I am called Nick.
> Then I can formulate the question: "What is the probability that the
> person called Nick should have a birth rank <=100, given that the
> real universe is one of type A, i.e. one where there are 200 people?"
> Now, this question cannot be ruled out on the grounds that
> probability assertions including personal pronouns are meaningless --
> for it contains no personal pronouns. Yet, this is enough to set the
> Doomsday argument rolling.

How do you know that every possible universes contains exactly one person
called Nick? Suppose you didn't, then the percentage of type B universes
that contains a person called Nick would be about twice the percentage of
type A universes that contains a person called Nick (since a type B
universe has twice as many people as a type A universe). Since these are
exactly the universes that would survive as possible universes after you
learn your name, this effect would cancel out the DA.

Let me give an example. Suppose in all possible universes everyone is born
conscious in the same mind state. One day after each person's birth he is
told his name. One day after that he is told whether his birth rank is <=
100. There are 200! type B universes, each corresponding to a different
assignment of 200 possible names to birth ranks. Similarly there are
200!/(100!100!) type A universes. Intuititvely in each universe every
person is randomly assigned a name that has not already been taken.

Consider someone just born who has a prior of 1/2 for the real universe
being type A. After learning his name, half of type A universes would be
assigned probability 0, so the probability of the real universe being type
A becomes 1/3. Then after learning his birth rank is <= 100, half of type
B universes drop out, so this probability goes back to 1/2.

-----End of forwarded message-----
Received on Fri Apr 17 1998 - 10:43:25 PDT