From: Robin Hanson (hanson@econ.berkeley.edu)
Date: Tue Aug 18 1998 - 13:22:52 MDT
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: *,#,@
* | 1 2 3 4 5 # | 1 2 3 4 5 @ | 1 2 3 4 5
------------- ------------- -------------
a | D D D D D a | D D D D D a | D D D D P
b | D D D D D b | D D D D D b | D D D D P
c | D M M M M c | D M M H D c | D M M H P
d | D M M M M d | D M H H D d | D M H H P
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
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: 510-643-2627
This archive was generated by hypermail 2.1.5 : Fri Nov 01 2002 - 14:49:28 MST