Category: time-and-causality
Type: puzzle
Associated thinker(s): William Newcomb, Robert Nozick
Original publication or approximate period: Formulated by Newcomb; published by Nozick in “Newcomb’s Problem and Two Principles of Choice” (1969)
Difficulty: Advanced
Themes: decision theory, prediction, causation
Related experiments: Laplace’s Demon; The Unexpected Hanging / Surprise Test
A transparent box contains $1,000. An opaque box contains either $1,000,000 or nothing. Yesterday, a highly reliable predictor filled the opaque box if it predicted you would take only that box, and left it empty if it predicted you would take both. You now choose the opaque box alone or both boxes. The contents are already fixed.
The predictor’s reliability is part of the setup, but perfect reliability is not required for many versions. You prefer more money. The challenge is deciding how to evaluate actions that are strongly associated with different contents while apparently unable to cause those past contents.
Should you take only the opaque box or take both when your decision is highly predictive of an already fixed reward?
The case distinguishes causal influence from evidence. It also exposes ambiguity in the instruction to maximize expected utility: different accounts use different probabilities to evaluate the same act. Debates about free choice sometimes enter the discussion, but the central issue is a conflict between decision principles.
Two-boxing: for each fixed content of the opaque box, taking both adds $1,000. Causal decision approaches emphasize that the present act does not fill yesterday’s box.
One-boxing: given the stipulated predictive connection, choosing only the opaque box is strong evidence that it contains the million. Evidential approaches evaluate the option using that correlation.
Model-sensitive response: specifying the predictor, causal structure, and what counts as an available intervention can clarify which probabilities are appropriate. Merely restating “maximize expected value” does not settle their interpretation.
One-boxers need not claim to change the past. Two-boxers need not deny that past one-boxers received more money in the stipulated record. A comparison of outcomes across differently predicted people differs from comparing acts while holding a particular box content fixed. Also, do not secretly let the predictor refill the box after the choice.
Transparent-box, imperfect-predictor, and medical common-cause variants probe different assumptions. Their recommendations can differ because the information and causal model differ. Treating them all as exactly the same problem prevents careful diagnosis.
The retrieved SEP decision-theory entry verifies the distinction between Newcomb’s formulation and Nozick’s 1969 publication. Dollar amounts are the standard illustrative scale. The article reports competing approaches without claiming an uncontested resolution.
Research check: 2026-10-30. References above were retrieved for the support described; this is an original educational explanation, not a substitute for the primary texts. Additional speculative comparisons are teaching prompts, not established historical variations.