Re: Doomsday Example

Nick Bostrom (
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.

I know, but in the example as I set it up, the slots *don't* have equal probability. Or so at least it seems to me. If you want to say that they do have equal probability then you also have to say that the fair coin in the C universe was almost certain to land on the side that creates an A universe, two times in a row. And if we expand the example to include m baby-universes, you have to say that the fair coin is almost certain to land on the same side m times in a row. Surely that is wrong.

Nick Bostrom Department of Philosophy, Logic and Scientific Method London School of Economics