Common-causes are not common common-causes

Philosophy of Science 69 (4):623-636 (2002)
Abstract
A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common-cause and it is shown that there exists pairs of correlated events probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common-cause. It is also shown that this conclusion remains valid even if one weakens slightly Reichenbach's definition of common-cause. The significance of the difference between common-causes and common common-causes is emphasized from the perspective of Reichenbach's Common Cause Principle.
Keywords Reichenbachian common cause
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DOI 10.1086/344625
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Relativistic Causality in Algebraic Quantum Field Theory.John Earman & Giovanni Valente - 2014 - International Studies in the Philosophy of Science 28 (1):1-48.
Causation, Measurement Relevance and No-Conspiracy in EPR.Iñaki San Pedro - 2012 - European Journal for Philosophy of Science 2 (1):137-156.
Minimal Assumption Derivation of a Weak Clauser–Horne Inequality.Samuel Portmann & Adrian Wüthrich - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (4):844-862.

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