# Re: Doomsday Example

Robin Hanson (hanson@econ.berkeley.edu)
Wed, 26 Aug 1998 11:55:06 -0700

Nick Bostrom writes:
>> >> >an A universe contains 10 humans and nothing else. A B universe contains
>> >> >10 humans and one trillion trillion stones. ...
>> >> >a small C universe ...spawns one thousand baby-univeses through a random
>> >> >process (like rolling fair dice) that has a 10% chance of yielding an
>> >> >A and 90% of a B.
>> >It seems clear that there will probably be about 100 A univeses and
>> >900 B universes.
>> Let N = "trillion trillion", and assume there are exactly 100 A
>> "universes" and 900 B "universes". ...
>> As described the only remaining uncertainty is where in this world I am.
>> If I treat stone slots and human slots equally, there are
>> 100*10 + 900(10+N) slots. If my prior is uniform across these slots, ...
>...
>consider the example that I formulated. It seems you have to say that
>when you find that you are a human, you have to conclude that all the
>1000 universes almost certainly are of type A. That means, you have
>to infer that the coin landed heads a thousand times. But is that
>really what you would infer? It seems very wrong.

I think you just haven't done the math here. I also think you meant to switch A and B in your first description. So 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. If we extend these descriptions to include which slot "I" occupy, we get 800 + 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."

Robin Hanson
hanson@econ.berkeley.edu http://hanson.berkeley.edu/ RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884 140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-8614