Doomsday Example (Was: Objection to the Doomsday Argument?)

Robin Hanson (
Tue, 18 Aug 1998 12:22:52 -0700

As promised, here is my formal example with a "neutral" prior.

Space has four slots: a,b,c,d
Time has five slots: 1,2,3,4,5
Each space/time combination can hold one of these: D(ead rock), M(onkey), H(uman), P(osthuman) Each "universe" describes what is at each space/time slot. Here are three universes: *,#,@

A state description says which universe I'm in, and which space-time slot I occupy. For example, I hope I'm @c4, and I'm glad I'm not #d5.

The prior is equal over all 60 states so defined.

My current information is "I'm in an H at time 4." Some I'm one of {#c4,#d4,@c4,@d4}. Given that, my posterior gives equal probability to universes #,@. These don't change if my information were "I'm an H."

If my info were "I'm an H or P," my posterior would say p(@) = 7/10, and p(#) = 3/10. If my info were "I'm an M, H, or P," I'd say p(*) = 8/24, p(#) = 6/24, p(@) = 10/24.

Just knowing I'm alive suggests (If I were smart enough to realize the implications) that I'm in a universe filled with life. Just knowing that I'm alive and smart suggests that I'm in a universe where intelligence prospers.

If I've understood Nick's preferred DA prior correctly, it gives the universes *,#,@ equal probability conditional on being in a slot filled with a H or P. Except he's not sure if that should instead be just H, or even M,H, or P.

If it's H or P, the priors must satisfy p(#) = (7/3)*p(@). Such a prior assumes "doom" is more probable, and seems designed to exactly counter act my joy that being smart suggests that I'm in a universe filled with smarts. But I'm not at all clear on why I should fiddle with my prior to do this.

Note also that Nick's rule doesn't specify what the prior is for the universe *, and we need that prior to learn things from the fact that our universe can evolve human life. Is there some more general rule here, or is the idea really just

"choose a full prior based on other considerations, and
then fiddle with it so being smart won't suggest your
universe has other smarts"?

Robin Hanson RWJF Health Policy Scholar, Sch. of Public Health 510-643-1884 140 Warren Hall, UC Berkeley, CA 94720-7360 FAX: 510-643-2627