# Re: Doomsday Example

Nick Bostrom (bostrom@ndirect.co.uk)
Sat, 29 Aug 1998 14:54:46 +0000

Robin Hanson wrote:

> >It doesn't really matter but it may be easiest to see the objection
> >that I'm trying to make if we assume the priors are:
> >
> >AA=1/4
> >AB=1/2
> >BB=1/4
> >
> >One can imagine this distribution arising from throwing a fair coin
> >in the C universe twice. This is the probabilities of the different
> >world combinations relative to an information set that only contains
> >the information about the set-up.
> >
> >Then, when you conditionalize upon being human (but you don't yet
> >have any other information), if you assume that you are a random
> >sample from all possible states/space-time slots (as you say we
> >should do), you get the posterior:
> >
> >AA=0
> >AB=0
> >BB=1
> >
> >in the limiting case where N is very large. (Reason: if there existed
> >an A universe, you would almost certainly have been one of the
> >stones.)
>
> No! You are confusing priors on universes with priors on states, even
> though I tried to clearly distinguish these in my previous post:

You can't assign priors on states and priors on universes independently. They are logically connected. For example, if there is a non-zero prior state probability that you are in state A-7, then there must be a non-zero prior universe probability that an A universe exists.

> >These "priors" are over worlds, but not necessarily over states.
> >If we extend these descriptions to include which slot "I" occupy,
> >we get 80 + 4N states. If I make the relative priors between states
> >equal to the relative "priors" between associated worlds, then, yes,
> >very little state prior is associated with the second world with two
> >B "universes." But conditioning on observing that I'm a human, I'm
> >back to estimating a 81% chance that there are two B "universes."
>
> If you're going to go with equal chance of A or B, then I'd say there
> are four possible worlds: AA, AB, BA, BB, and 80 + 4N space-time slots
> among these worlds. Giving equal probability to these *slots*, then
> conditioning on being human, you get equal probability to be in A vs. B.

Nick Bostrom
http://www.hedweb.com/nickb n.bostrom@lse.ac.uk Department of Philosophy, Logic and Scientific Method London School of Economics