The Newcomb Problem Has No Agreed Answer

In 1960, physicist William Newcomb described a thought experiment to his friend Robert Nozick. Nozick published it in 1969, and it has been splitting decision theorists ever since.

A highly reliable predictor places two boxes before you. Box A is transparent: it contains $1,000. Box B is opaque. The predictor has already decided its contents: 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 prediction was made yesterday. Whatever is in Box B is now fixed. You cannot change it.

Do you take both boxes, or only Box B?

Two-boxers argue from causal reasoning: the predictor's decision is done. The money is either there or it isn't. Your choice today cannot cause a change in yesterday's box. Taking both boxes strictly dominates — it is better by $1,000 in every possible state of the world. Economists and game theorists lean this way.

One-boxers argue from evidential reasoning: in the situations where people take one box, they reliably walk away with a million dollars. In the situations where people take two boxes, they reliably walk away with a thousand. Choosing to be a one-boxer is strong evidence that you are the kind of person the predictor filled the closed box for. Many philosophers and some statisticians lean this way.

The philosophical issue is whether rational choice should track causal consequences or evidential correlations. Both positions are internally consistent. The thought experiment was designed to reveal that standard decision theory hadn't settled which one grounds rationality.

Nozick noted in 1969 that almost everyone finds one answer obvious — and almost no one agrees on which one.