From: Nick Bostrom (bostrom@ndirect.co.uk)
Date: Fri Aug 28 1998 - 11:08:34 MDT
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
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