# Re: Doomsday Example

Robin Hanson (hanson@econ.berkeley.edu)
Thu, 20 Aug 1998 09:50:06 -0700

>> >In #d5 there's a dead rock! - "Hurray! I'm so happy that I did
>> >not turn out to be a rock." But is it even a meaningful hypothesis
>> >for you to think that you could be a dead rock? I can't make any
>> >sense of that "possibility".
>>
>> But this makes clear sense to me, and I think is a key reason
>> for our divergent views. The atoms that constitute me could have
>
>That is true, but then they would not have been you.
>
>> I find
>> it quite possible that I could have never existed.
>
>That is also true, but it doesn't imply 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 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.

>Notice that after ruling out world *, the two remaining worlds are
>equally probable for you. I.e., you should think that the likelihood
>that you exist is equally great given world # as given world @. In
>both cases it is one.
>
>Why? Because you are not a random sample from all possible observers;
>only from all actual observers.

I don't accept as a fundamental axiom any statement of the form "I am a random sample from X." As far as I'm concerned the rational way to do inference is to construct a state space with associated observer information partitions, put a prior over the state space, and then turn the crank. The result of this might or might not have me being a random sample from some set.

As I said, I don't want to reason about random samples at all. But I *do* want to reason like this:

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