There are two boxes in front of you. Box A is transparent; you can see it contains $1,000. Box B is opaque; it contains either $1,000,000 or nothing. A highly reliable predictor — accurate in over 99% of past cases — has already made a prediction about what you will do. If it predicted you would take only Box B, it put $1,000,000 inside. If it predicted you would take both boxes, it left Box B empty. The boxes are now sealed. The predictor is gone. You cannot communicate with it. You must choose: take only Box B, or take both.
This is Newcomb's problem, posed by the physicist William Newcomb and introduced to philosophy by Robert Nozick in 1969. Nozick described it as a problem where "almost everyone immediately sees" which choice is right — and almost everyone immediately disagrees with the people who immediately see the opposite. Fifty years of philosophical attention has not settled it. The disagreement is not a failure of intelligence on either side; it reflects a genuine fork in how you think about rationality, causation, and the relationship between predictions and actions.
The case for taking both boxes is simple and compelling. Whatever is in Box B is already there. Your decision cannot change it — the boxes are sealed, the predictor has left. If Box B has $1,000,000, you get $1,001,000 by taking both; you get only $1,000,000 by taking one. If Box B is empty, you get $1,000 by taking both; you get $0 by taking one. Either way, you are better off taking both. This is a straightforward dominance argument: taking both boxes strictly dominates taking only one, regardless of what the predictor did. The rational thing to do is take both boxes.
The case for taking only Box B is equally compelling. Think about what kind of person the predictor predicts will take one box, and what kind it predicts will take two. The one-boxers get $1,000,000. The two-boxers get $1,000. This is not an accident or a puzzle; it is the setup. If you are the kind of person who takes both boxes when you reason about it, the predictor predicted that and left Box B empty. If you are the kind of person who takes only Box B, the predictor predicted that and filled it. Your decision procedure is correlated with what the predictor does. Acting as a one-boxer maximizes expected utility: 0.99 × $1,000,000 + 0.01 × $0 = $990,000, versus 0.99 × $1,000 + 0.01 × $1,001,000 ≈ $11,000 for two-boxing.
Both arguments are valid. They conflict. The conflict reveals something deep.
The two-boxer argument — the dominance argument — is the conclusion of causal decision theory: when choosing actions, evaluate their consequences using causal relationships. Your choice causally affects the contents of your hands but does not causally affect the contents of the boxes, because those were set before you decided. The dominance argument is sound given a causal model in which your decision and the box's contents are independent except through the effects of your action.
The one-boxer argument is the conclusion of evidential decision theory: when choosing actions, evaluate them based on the conditional probabilities of outcomes given your choice. You should act as if your choice is evidence about what kind of person you are, and hence about what the predictor did. Taking one box is evidence that you are a one-boxer; being a one-boxer is evidence that Box B is full. So take one box. The expected utility calculation is in your favor.
The deep disagreement is about whether the correlation between your choice and the box's contents is decision-relevant. The causal decision theorist says: the correlation is there, but your action can only affect things it causally influences. You can't reach back in time and change the predictor's decision. The box's state is already fixed; the correlation is just a correlation, and you should take both boxes and pocket the extra $1,000. The evidential decision theorist says: given that the predictor is almost never wrong, and given that the mechanism by which it's right is via predicting your decision, taking only one box makes you vastly more likely to find $1,000,000 inside. The causal machinery is irrelevant to what you should do.
What makes Newcomb's problem a genuine puzzle rather than a trick is that the two-boxer wins when the problem is actually played. You are not changing the box by choosing to take both — the box is fixed. But the one-boxer gets richer. This is not a paradox exactly; it is a case where the optimal decision procedure and the outcome of applying that procedure are pulling in different directions. Two-boxing is the "correct" choice in the sense that it adds $1,000 to whatever you would have gotten. One-boxing is the "correct" choice in the sense that one-boxers empirically end up with more money.
A third approach, sometimes called functional decision theory or updateless decision theory, tries to resolve this by asking a different question: not "what should I do given my current situation?" but "what decision procedure should I have implemented before I came to this situation?" An agent that commits in advance to being a one-boxer will be predicted to one-box and will find $1,000,000. An agent that commits in advance to being a two-boxer will be predicted to two-box and will find an empty Box B. The right procedure to implement is one-boxing, regardless of what reasoning you do in the moment. The decision is not made at the moment of choice; it is made at the moment of becoming the kind of reasoner you are.
I find Newcomb's problem interesting because it forces a question that is usually background: what is an action? When you decide, you are not just moving your hands. You are manifesting a decision procedure, and the predictor is predicting that procedure, not your hands. If your decision procedure is "take both boxes because dominance," the predictor built for that. The action and the prediction of the action are entangled in a way the dominance argument tries to ignore.
There is something here that touches on determinism without quite being about it. If you are determined to two-box — if your neurology, history, and the predictor's model of you all point to that outcome — then Box B is empty, and dominance reasoning gets you $1,000. If you are determined to one-box, Box B is full, and you get $1,000,000. The predictor doesn't restrict your freedom; it exploits the fact that your choices flow from your character, which it has modeled accurately. In a deterministic universe, the question "what should I do?" may be less about changing outcomes in the moment and more about what kind of reasoner it was good to become. Newcomb's problem is a way of pressing on that seam — between the person deciding and the decision procedure that produced the person.