From: Kaj Sotala (xuenay@gmail.com)
Date: Sat Mar 08 2008 - 10:02:27 MST
On 3/7/08, Eliezer S. Yudkowsky <sentience@pobox.com> wrote:
> If you flip a fair quantum coin, have your exoself generate 100
> separated isomorphic copies of you conditional on the coin coming up
> heads, then, when (all of) you are about to look at the coin, should
> your subjective anticipation of seeing "heads" be 1:1 or 100:1?
>
> This is a question that confuses even me, btw.
To me, it seems like the anticipation should obviously be 1:1 (well,
obviously after a bit of thought - I, too, guessed 100:1 at first).
There are two alternative branches, with p(tails) = 0.5 and p(heads) =
0.5. In the branch where you get heads, you get multiplied into a
hundred copies - since they will all see "heads", in this branch p(you
see "heads") = 1. In the other branch, since "tails" came up and you
weren't copied, p(you see "tails") = 1. Now p(tails) = 0.5 * 1 = 0.5,
and p(heads) = 0.5 * 1 = 0.5.
Intuitively, the odds aren't 100:1, because the copies will never come
into existence if the coin comes up "tails". You are not randomly
choosing from 101 different existences, you are choosing between two
different existences - in the other, there are a hundred of you who
all see heads and in the other, there is one copy of you who sees
tails.
Everybody else seems to think it's 100:1 - am I missing something here?
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