Newcomb's paradox

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 or not the problem is actually a paradox is disputed.

The problem

There are two players named Predictor and Chooser. Chooser is presented with two boxes: an open box containing $1,000, and a closed box that contains either $1,000,000, or $0 (he doesn't know which). Chooser must decide whether he wants to be given the contents of both boxes, or just the contents of the closed box.

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The complication is that the day prior, Predictor predicts how Chooser will choose. If he predicts that Chooser will take only the closed box, then he will put $1,000,000 in the closed box. If he predicts that Chooser will take both boxes, he will leave that box empty. Chooser knows this rule of Predictor's behavior, but he does not know Predictor's actual prediction.

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The question is: should Chooser take just the closed box or take both boxes?

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If Predictor is 100% accurate and if Chooser takes only the closed box, he will get $1,000,000. If Chooser takes both boxes, the closed box will be empty and Chooser only gets $1,000. Even if the Predictor is only mostly accurate, Chooser may still not want to risk only getting $1,000. By this reasoning, Chooser should only choose the closed box.

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But at the time when Chooser walks up to the boxes the contents have already been set. The closed box is either empty or full. It's too late for the contents of the boxes to change. Chooser might as well take whatever's in both boxes. Whether the closed box is empty or full, he'll clearly make $1,000 more by choosing both boxes than by choosing just one box. By this reasoning, Chooser should always choose both boxes.

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In his 1969 article, Nozick noted that "To almost everyone, it is perfectly clear and obvious what should be done. The difficulty is that these people seem to divide almost evenly on the problem, with large numbers thinking that the opposing half is just being silly."

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