From: Eliezer S. Yudkowsky (sentience@pobox.com)
Date: Tue Apr 29 2003 - 17:38:05 MDT
Rafal Smigrodzki wrote:
>
> You know that half of all civilizations die at age 10 billion persons, and
> the other half live to 10 trillion persons.
>
> You know that you are a sentient belonging to one of these civilizations.
> There is a sealed envelope in front of you, containing your birth rank.
>
> What is the a priori probability of being in the doomed civ?
>
> 10e9
> P(X)=------------- ~ 0.001
> 10e11 + 10e9
>
> Your a priori probability of being doomed is small, because you know that
> most people live in the happy majority
>
>
> You open the envelope, find the number 999 999 999, and update your
> probabilities:
>
> (1-.5)1/10e9
> ----------------------------- ~ 0.99
> (1-.5)*1/10e9 + (1-.5)*1/10e11
>
> Your a posteriori probability of being doomed if your birth rank is 999 999
> 999, is 99%. Please note, that you didn't move a lightspeed from one
> civilization to another, merely adjusted your point of view based on the
> data that became available.
Er... Rafal, shouldn't that be:
> (1/10e9)*10e9
> ----------------------------- ~ 0.5
> (1/10e9)*10e9 + (1/10e11)*10e11
I don't know where you're getting the (1-.5) from, since it's neither a
prior nor a conditional probability. And the end answer is, of course,
0.5, which corresponds to the reality that half of all people with
birthrank 999,999,999 live in short-lived civilizations, and half live in
long-lived civilizations.
-- Eliezer S. Yudkowsky http://singinst.org/ Research Fellow, Singularity Institute for Artificial Intelligence
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