all of me or one of me

From: Wei Dai <weidai.domain.name.hidden>
Date: Thu, 1 Apr 1999 17:56:15 -0800

Given the MWI or one of the "everything" theories we've discussed, the
universe must contain multiple observers who have exactly the same
memories and experiences as you do. Should you identify with all of them,
or should you think, "I am one of these people, but I don't know which"?

I think the following thought experiment shows the latter is more
appropriate. Suppose you are one of two people in a prisoner's dilemma
type game, where if you push button A both players will get 4 dollars, but
if you push button B you will get 5 dollars and the other player will get
nothing. The twist is that both players are given temporary amnesia and
are put into identical rooms so you don't know what your identity is.

If you identify with both players, then you should press A. However I
think most people under the circumstances will press B. This implies
people must condition their goals (utility functions) on their identities.
That is, they must think like this:

There is equal probability that I am player 1 or player 2. If I am player
1, then I want to maximize player 1's payoff. If I am player 2, then I
want to maximize player 2's payoff. If I press A, my expected utility is
.5*4+.5*4=4 (plus 4 if the other player pushes A). If I press B, my
expected utility is .5*5+.5*5=5 (plus 4 if the other player pushes A).
Therefore I should press B.

I don't think it is possible to obtain this result if each player has only
one unconditional utility function defined over states of the universe.
This seems to imply that traditional decision theory is incomplete.
Received on Thu Apr 01 1999 - 17:57:43 PST