What Does Newcomb's Paradox Teach Us?

15 Pages Posted: 16 Apr 2009 Last revised: 12 Mar 2010

See all articles by Gregory Benford

Gregory Benford

University of California, Irvine

David Wolpert

Santa Fe Institute

Date Written: February 26, 2010


In Newcomb's paradox you choose to receive either the contents of a particular closed box, or the contents of both that closed box and another one. Before you choose, a prediction algorithm deduces your choice, and fills the two boxes based on that deduction. Newcomb's paradox is that game theory appears to provide two conflicting recommendations for what choice you should make in this scenario. We analyze Newcomb's paradox using a recent extension of game theory in which the players set conditional probability distributions in a Bayes net. We show that the two game theory recommendations in Newcomb's scenario have different presumptions for what Bayes net relates your choice and the algorithm's prediction. We resolve the paradox by proving that these two Bayes nets are incompatible. We also show that the accuracy of the algorithm's prediction, the focus of much previous work, is irrelevant. In addition we show that Newcomb's scenario only provides a contradiction between game theory's expected utility and dominance principles if one is sloppy in specifying the underlying Bayes net. We also show that Newcomb's paradox is time-reversal invariant; both the paradox and its resolution are unchanged if the algorithm makes its 'prediction' after you make your choice rather than before.

Keywords: Newcomb's paradox, game theory, Bayes net, causality, determinism

JEL Classification: A12, C11, C70, C72

Suggested Citation

Benford, Gregory and Wolpert, David, What Does Newcomb's Paradox Teach Us? (February 26, 2010). Available at SSRN: https://ssrn.com/abstract=1381295 or http://dx.doi.org/10.2139/ssrn.1381295

Gregory Benford

University of California, Irvine ( email )

Campus Drive
Irvine, CA 62697-3125
United States

David Wolpert (Contact Author)

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 897501
United States

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