Re: Doomsday Example

Nick Bostrom (
Sat, 22 Aug 1998 02:30:29 +0000

Robin Hanson wrote:

> Nick B. continues are interesting conversation:

Yes, it has all the right ingredients :-)

> But nothing else could have been me exactly. The only thing that
> could be me exactly is something born when I was, and which then
> did everything I did afterward, including writing this message.

How does that support your claim that it makes sense to say that you could have been a rock?

> >> What prior would you assign to world * in my example?
> >
> >That depends on such things as simplicity etc. If the three worlds
> >are equal in these repects, I would say P(*) = 1/3. This would be the
> >absolute prior. Then you take account of the fact that you exist, and
> >you rule out world * (though I'm not sure what do about the monkeys).
> >Then you renormalize and get P(#) = P(@) = 1/2.
> But your *prior* is before you take information into account, and you
> seem to prefer p(*) = 1/3, p(#) = 7/20, p(@) = 3/20. I instead prefer
> all three being 1/3. You say:

But I too would say all absolute priors three are 1/3. But these are the probabilities you should assign if you knew absolutely nothing, not even that you existed. In practice, you will always know you exist. If you conditionalize on this information then you get p'(*)=0, p'(#)=p'(@)=1/2. Now if you want you can call this new probability distribution, p'=p( _ | "I exist."), your "prior". (What information you include in the "prior" depends at the task at hand.)

At this stage you will want to consider conditional probabilities such as:

p'("I'm in world # at position 4d."| "I'm in world #.")

Do the same for world @. Then inverst these conditional probabilities with Bayes' theorem. Then suppose you find out that you live at time 4. Use this information to update your the conditional probabilities. What you get is the doomsday conclusion!

> >I'm not sure our disagreement is best described as being about priors.
> But in this example the disagreement is exactly about priors, unless
> you want to dispute my choice of state space or information partitions.
> My prior gives my preferred result, yours gives your preferred result.

But now it seems you and I have the same priors for all the worlds.

To say "I exist." is like saying "That exists." while
> >pointing to some object, say a stone. Surely you would not reason
> >like this:
> >
> >"That exists [pointing to a stone]. It can be considered a random
> >sample of all possible stones. Hence there are probably a great many
> >stones."
> >
> >And yet you to want to reason like this:
> >
> >"I exist [pointing to yourself]. I can be considered a random sample
> >from all possible observers. Hence there are probably a great many
> >observers."
> >
> >Both these arguments seem equally wrong to me.
> As I said, I don't want to reason about random samples at all.
> But I *do* want to reason like this:
> "I'm not sure how many stones a universe has, but I expect universes
> that have more stones in one region to have more stones in other regions
> as well. If I look in one spot in this universe and I find a stone, that
> suggests I'm more likely to find stones at other spots in this universe
> as well."

Sure, but this reasoning only works for things that may or may not be present where there are observers. Stones are a good example. But many other phenomena are correlated with the presense of observers and then this reasoning doesn't work. For instance, as you yourself has argued in your "Must early life be easy?"-paper, it would be wrong to use the observation that evolutionary processes here on Earth were fairly quick to infer that quick evolutionary processes are common in the universe; for we would not have existed if the particular evolutionary process we observe had not been quick enough to happen before the sun becomes a red gigant.

Now, of all phenomena imaginable, none has a stronger correlation with the presense of observers than the presense of observers. And yet you want to use the presense of this observer, Robin Hanson, to infer that there are probably many observers! This looks like an extreme form of the same mistake you warn against in your paper.

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