sasw@bnl.UUCP (Steven Akiba Swernofsky) (11/03/83)
This problem (the "Newcomb situation") was presented in Sci. Am. in
the old Mathematical Games column. It is true that the "math" is
easy, but this remains a problem for decision theory, not religion.
The game is drawn with two players. Each has two choices:
opponent
zonk prize
modest 0 1,000,000
YOU
greedy 1,000 1,001,000
Now there are two ways to view this problem: The first is simple --
since the "greedy" strategy is uniformly better than the "modest" one,
you should pick it.
But, the second is also simple -- you are told that your opponent is
VERY good at his prediction. Let us say 95% accurate. If you take
the "modest" strategy, you will win (on the average) .95 of 1 million,
= 950,000. The "greedy" strategy will win .95 of 1,000 plus .05 of
1,001,000 = 51,000. You should therefore pick the "modest" strategy.
So, there is a contradiction. Two perfectly good ways of making your
decision produce clearly opposite results! What is the problem?
I think the answer lies in the characterization of the opponent's
choice as having been "already made" when you pick. If your opponent
(the "superior being") is THAT good, we would be better off thinking
about this problem as if the opponent actually got to decide AFTER
you choose, and not before. Since your decision matters so much (even
only probabalistically) to your opponent's decision, treating the
problem as a choice between X and X + 1,000 is a mistake. I would
take the "modest" strategy.
-- Steve