Do the bell inequalities require the existence of joint probability distributions?

Philosophy of Science 55 (3):387-401 (1988)
Fine has recently proved the surprising result that satisfaction of the Bell inequality in a Clauser-Horne experiment implies the existence of joint probabilities for pairs of noncommuting observables in the experiment. In this paper we show that if probabilities are interpreted in the von Mises-Church sense of relative frequencies on random sequences, a proof of the Bell inequality is nonetheless possible in which such joint probabilities are assumed not to exist. We also argue that Fine's theorem and related results do not impugn the common view that local realists are committed to the Bell inequality
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DOI 10.1086/289443
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Soazig Le Bihan (2009). Fine's Ways to Fail to Secure Local Realism. Studies in the History and Philosophy of Modern Physics 40 (2):142-150.

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