Re: Doomsday Example

Nick Bostrom (bostrom@ndirect.co.uk)
Fri, 28 Aug 1998 17:08:34 +0000

Robin Hanson wrote:

> I'll assume A universes
> have 10 humans + N stones, and B universes have just 10 humans.
>
> I don't want to work out the math for 1000 universes, but two should be
> enough to see what works. In that case there are four possible worlds:
> -- Two A "universes", with 2*(10+N) space-time slots, and "prior" of 1%.
> -- Two B "universes", with 2*10 slots, and "prior" 81%.
> -- An A and a B "universe," with 2*10 + N slots, and "prior" 9%.
> -- Another possible world that looks just like the last one.
> These "priors" are over worlds, but not necessarily over states.

I'm not sure where you got these priors from. 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.)

Now, this seems clearly wrong. I conclude that you should not include all space-time slots in the reference class, but only those containing observers.


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