Betting on the outcomes of measurements: A bayesian theory of quantum probability

Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):395-414 (2002)
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Abstract

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance, the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles. These include the uncertainty principle and the violation of Bell's inequality among others. Quantum gambles are closely related to quantum logic and provide a new semantics for it. We conclude with a philosophical discussion on the interpretation of quantum mechanics.

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Citations of this work

QBism and the limits of scientific realism.David Glick - 2021 - European Journal for Philosophy of Science 11 (2):1-19.
Subjective probability and quantum certainty.Carlton M. Caves, Christopher A. Fuchs & Rüdiger Schack - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):255-274.
Entropy - A Guide for the Perplexed.Roman Frigg & Charlotte Werndl - 2011 - In Claus Beisbart & Stephan Hartmann (eds.), Probabilities in Physics. Oxford University Press. pp. 115-142.
Two dogmas about quantum mechanics.Jeffrey Bub & Itamar Pitowsky - 2007 - In Simon Saunders, Jonathan Barrett, Adrian Kent & David Wallace (eds.), Many Worlds?: Everett, Quantum Theory & Reality. Oxford University Press.
Probabilism for stochastic theories.Jer Steeger - 2019 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 66:34–44.

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References found in this work

The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
Truth and probability.Frank Ramsey - 2010 - In Antony Eagle (ed.), Philosophy of Probability: Contemporary Readings. New York: Routledge. pp. 52-94.
The Foundations of Statistics.Leonard J. Savage - 1956 - Philosophy of Science 23 (2):166-166.
The Foundations of Statistics.Leonard J. Savage - 1954 - Synthese 11 (1):86-89.

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