Newcomb's Problem

Newcomb's problem is a famous puzzle in decision theory. The basic set-up is that a super-intelligence of some sort (a super-neuroscientist, a psychic, God, a super-computer, Omega, whatever) offers to play a game with you. The intelligence puts a box and a thousand dollars on a table. Either the box contains a million dollars or it is empty (or in special circumstances, it contains a high-yield explosive). The intelligence tells you that you may have either the contents of the box -- the one-box choice -- or you may have both the contents of the box and the thousand dollars -- the two-box choice. But there is a catch. The intelligence tells you that if it predicts you will take both the box and the thousand dollars, then it has put nothing in the box. If, however, the intelligence predicts that you will take only the contents of the box, then it filled the box with a million dollars. (Any fancy choosing -- like flipping a coin or calling in a friend -- is punished: if the intelligence predicted that you would do something fancy, then it filled the box with a high-yield explosive.) Suppose for the purposes of the thought experiment that you have excellent evidence that the intelligence is a very reliable predictor: a range of values work here, but to be concrete, suppose the intelligence predicts correctly nine times out of ten. The question is whether you should make the one-box choice or the two-box choice.

Decision theorists line up on both sides. Evidential decision theorists point out that conditioning on the two possible acts -- the one-box choice or the two-box choice -- the act that maximizes expected utility is the one-box choice. Hence, one should take just the contents of the box. Causal decision theorists point out that the content of the box at the time of the choice does not causally depend on the choice being made. Whatever the intelligence put in the box is there. Choosing to take or not to take the contents of the box won't change whatever's in it. Moreover, whatever happens to be in the box, taking both the box and the thousand dollars dominates taking just the contents of the box.

A large and growing literature has developed around Newcomb's problem. I will not try to cover even the most basic issues here. (For example, I'm not going to try to address pre-commitment.) What I want to do is ask a simple question: Why does Newcomb's problem need the box at all?

As far as I can tell, the problem is left completely unchanged by putting it as follows. A super-intelligence wants to play a game with you. The intelligence scans you and predicts whether you will take exactly one million dollars from the table. If the intelligence thinks that you will take exactly one million dollars, then it places $1,001,000 on the table. Otherwise, it places $1,000 on the table. Question: As you stand in front of the table, do you take all of the money in front of you or not?