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Outlawing Anthropics: An Updateless Dilemma

26 Eliezer_Yudkowsky 08 September 2009 06:31PM

Let us start with a (non-quantum) logical coinflip - say, look at the heretofore-unknown-to-us-personally 256th binary digit of pi, where the choice of binary digit is itself intended not to be random.

If the result of this logical coinflip is 1 (aka "heads"), we'll create 18 of you in green rooms and 2 of you in red rooms, and if the result is "tails" (0), we'll create 2 of you in green rooms and 18 of you in red rooms.

After going to sleep at the start of the experiment, you wake up in a green room.

With what degree of credence do you believe - what is your posterior probability - that the logical coin came up "heads"?

There are exactly two tenable answers that I can see, "50%" and "90%".

Suppose you reply 90%.

And suppose you also happen to be "altruistic" enough to care about what happens to all the copies of yourself.  (If your current system cares about yourself and your future, but doesn't care about very similar xerox-siblings, then you will tend to self-modify to have future copies of yourself care about each other, as this maximizes your expectation of pleasant experience over future selves.)

Then I attempt to force a reflective inconsistency in your decision system, as follows:

I inform you that, after I look at the unknown binary digit of pi, I will ask all the copies of you in green rooms whether to pay $1 to every version of you in a green room and steal $3 from every version of you in a red room.  If they all reply "Yes", I will do so.

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