From: Lee Daniel Crocker (lee@piclab.com)
Date: Tue Apr 29 2003 - 16:31:06 MDT
> (Eliezer S. Yudkowsky <sentience@pobox.com>):
>
> Suppose we implement this rule.
>
> There are two fourth balls. The fourth ball from the short sequence looks
> at itself, follows your argument, and says, "I must be in the short
> sequence!" The fourth ball from the long sequence looks at itself,
> follows your argument, and says, "I must be in the short sequence!"
>
> We therefore find that the gts-conclusion "I must be in the short
> sequence!" calibrates to an actual 50% chance of being in the long sequence.
Here you're confusing sample spaces. The DA makes the assumption that
you are a random sample from everyone who has ever lived or will
live _in your universe_, and the conclusion we want to draw is the
nature of this universe compared to all other possible universes, of
which we further assume our universe is a random sample. It _does not_
assume that you are a random sample from all people in all universes.
To make it clearer: Mr. Gumball, I inform you that there are two
gumball machines, one with 10 gumballs and one with 1 million. I
have selected you randomly _from among all gumballs in both machines_,
and you are number four. I'll give you $100 if you can guess which
machine you're in. How much will you pay to play this game? The
correct answer is, as you say, $50.
But now I change to game to coincide with the DA: Mr. Gumball, I
flipped a fair coin and chose one of the two gumball macines that
exist. Then, I randomly selected you as a sample _from that machine_,
and that machine only. You are number 4. Same offer. Now how much
would you pay to guess which machine I chose in step 1? Now the
correct answer is comsiderably more than $50, in fact it's more than
$99.99 (100,000 / 100,001, to be exact).
-- Lee Daniel Crocker <lee@piclab.com> <http://www.piclab.com/lee/> "All inventions or works of authorship original to me, herein and past, are placed irrevocably in the public domain, and may be used or modified for any purpose, without permission, attribution, or notification."--LDC
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