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Published May 8, 2000 | Accepted Version
Journal Article Open

Quantum probability from decision theory?

Abstract

In a recent paper, Deutsch claims to derive the 'probabilistic predictions of quantum theory' from the 'non–probabilistic axioms of quantum theory' and the 'nonprobabilistic part of classical decision theory.' We show that his derivation includes a crucial hidden assumption that vitiates the force of his argument. Furthermore, we point out that in classical decision theory a standard set of non–probabilistic axioms is already sufficient to endow possible outcomes with a natural probability structure. Within that context we argue that Gleason's theorem, relying on fewer assumptions than Deutsch, provides a compelling derivation of the quantum probability law.

Additional Information

© 2000 The Royal Society. Received 13 July 1999; revised 11 November 1999; accepted 10 December 1999. This work was supported in part by the the US Office of Naval Research (grant no. N00014-1-93-0116) and the US National Science Foundation (grant no. PHY-9722614). H.B. is partly supported by the Institute for Scientific Interchange Foundation (ISI) and Elsag-Bailey, and C.A.F. acknowledges the support of the Lee A. DuBridge Prize Postdoctoral Fellowship at Caltech. C.M.C., C.A.F. and R.S. thank the Isaac Newton Institute for its hospitality, H.B. thanks the ISI for its hospitality, and J.F. acknowledges the hospitality of Lawrence Berkeley National Laboratory.

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