Newcomb’s Problem

Assume in this thought experiment that you have strong reasons to regard the predictor as almost always correct, including in this situation. The transparent box always contains €1,000. Before your choice, the predictor puts €1,000,000 in the opaque box if it predicts that you will choose only that box, and nothing if it predicts that you will choose both. You then choose the opaque box alone or both. You do not change the earlier filling, but you do choose which money to take.

This is a canonical unresolved problem in decision theory, not an empirical paradox with a single solution. Practical transfer requires predictor-conditioned environments with clear timing.

In this protocol, your choice can provide evidence about the earlier box contents without causing those contents. The causal comparison holds the contents fixed; the evidential comparison incorporates their association with the prediction. This distinction does not settle which decision rule is correct.

AI transfer to investigate: If an AI system predicts behaviour reliably enough in a bounded task and allocates resources beforehand, we can test how users distinguish prediction from causal influence. That predictive reliability must be established separately; it does not follow from Newcomb’s thought experiment.

Proposed test, not yet conducted: Create predictor-conditioned allocation tasks and vary whether the causal structure is shown explicitly. Measure mistaken causal attribution and choice.

Use Newcomb primarily to keep prediction, correlation and intervention distinct — not to declare one decision theory settled.

Prediction and box allocation precede the choice. The choice does not change the past. Causal and evidential decision rules remain philosophically contested.

Nozick (1969), Newcomb’s Problem and Two Principles of Choice, pp. 114–116: reliability assumption and timing; p. 134: no backwards causation.

Nozick’s text specifies the predictor’s reliability, the sequence of events and the absence of backward causation. Amounts are expressed in euros for this example. The thought experiment does not establish the predictive reliability of existing AI systems.