Definition
The Newcomb problem is a decision puzzle in which two respectable principles of rational choice — maximising expected utility and choosing a dominant action — give directly opposite recommendations. It is a stress test for decision theory.
The setup involves a highly reliable predictor and two boxes. One box is transparent and visibly contains a small sum. The other is opaque and contains either a large sum or nothing, depending on what the predictor forecast you would do. You may take just the opaque box, or take both boxes.
Why it matters
How it works
The predictor has already made its forecast and the contents of the opaque box are now fixed. The dominance argument exploits this: since you cannot change what is in the box, taking both boxes yields strictly more in every state. The expected-utility argument exploits the predictor's reliability: choosing one box is strong evidence that the box is full, so the conditional expected payoff of one-boxing is far higher.
Priest uses the problem to show that "rational choice" is not a single settled notion. Evidential decision theory weights outcomes by probabilities conditional on the action; causal decision theory insists on probabilities of states the action can actually influence. The Newcomb problem is precisely the case where these two readings of expected value come apart.