Newcomb's paradox

In philosophy and mathematics, Newcomb's paradox, also referred to as Newcomb's problem, is a thought experiment involving a game between two players, one of whom purports to be able to predict the future. Whether the problem actually is a paradox is disputed.

Newcomb's paradox was created by William Newcomb of the University of California's Lawrence Livermore Laboratory. However, it was first analyzed and was published in a philosophy paper spread to the philosophical community by Robert Nozick in 1969, and appeared in Martin Gardner's Scientific American column in 1974. Today it is a much debated problem in the philosophical branch of decision theory.

A person is playing a game operated by the Predictor, an entity presented as somehow being exceptionally skilled at predicting people's actions. The player of the game is presented with two boxes, one opaque (labeled A) and the other transparent (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box A. Box B contains a visible $1,000. The contents of box A, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box A, or both boxes. If the Predictor predicts that both boxes will be taken, then box A will contain nothing. If the Predictor predicts that only box A will be taken, then box A will contain $1,000,000.

Nozick also stipulates that if the Predictor predicts that the player will choose randomly, then box A will contain nothing.

By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box A have already been determined. That is, box A contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box A, the fact that its contents are based on the Predictor's prediction, and knowledge of the Predictor's infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box A are.

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