Re: Doomsday Example

Nick Bostrom (
Tue, 25 Aug 1998 02:34:12 +0000

Robin Hanson wrote:

> Nick Bostrom writes:
> >Suppose we change the example slightly. Now, an A universe contains
> >10 humans and nothing else. A B universe contains 10 humans and one
> >trillion trillion stones. There is a small C universe (of negligible
> >size), and it 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.
But that means about 90% of all humans will find
> >themselves in an B universe. So if all you knew was the set-up and
> >that you were a human, then you should believe that there was a
> >90% chance that you were in an B universe.
> >
> >And yet, if you include stones in the reference class, then it seems
> >you should believe you are in an A universe. For if you are in a B
> >universe, then there exists in total at least one trillion trillion
> >stones and then you would probably have been one of these stones
> >rather than a human.
> Let N = "trillion trillion", and assume there are exactly 100 A
> "universes" and 900 B "universes". Note that these are *not* "universes"
> in the sense I was using of "possible worlds."

Sure, my usage agrees with this.

> The entire construction
> of C + 100 As + 900 Bs is just one total space-time, a "possible world."
> 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,

But the point of my example having a C universe etc. was that this prior is not a plausible one. The fair dice in the C universe, or rather let's say it's a fair coin, do you really want to say that the prior probability that this coin should land heads all thousand throws is almost one? That seems wrong.

> then conditioning on my being in a human slot, there is a 90% chance I'm
> in a B "universe," as you prefer.

But since that prior seems wrong, you don't get this result.

> >> >Similarly, I would say that finding that you are an observer does not
> >> >give you reason for thinking that a large fraction of all slots in
> >> >the universe is occupied by observers.
> >>
> >> Your error is to say "large fraction." The fact that life exists
> >> on Earth *does* make it more likely that our universe has other planets
> >> where life has evolved in a similar time. It just isn't enough to
> >> conclude the fraction of Earth-like planets with life is "large."
> >...
> >And now you say that finding that life exists on Earth should
> >not affect your beliefs about about the fraction of Earth-like
> >planets with life.
> But I said exactly the opposite in the quote above!

Actaully, you didn't say anything about what we should believe about the *fractions*.

Suppose the only alternatives were (1): one in ten Earth-like planet evolve intelligent life; or (2) one in a thousand does. Suppose the prior probability is fifty-fifty.

Now you observer that the Earth has evolved life. Based on your clarification above, I now take it that you think this observation should increase your confidence in (1). Is this right?

But then what happened to the selection-effect you spoke of in the "Early life"-paper? "Since no one on Earth would be wondering about the origin of life if Earth did not contain creatures nearly as intelligent as ourselves, the fact that four billion years elapsed before high intelligence appeared on Earth seems compatible with any expected time longer than a few billion years"

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