The principle of the common cause faces the Bernstein Paradox

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I consider the problem of extending Reichenbach's principle of the common cause to more than two events, vis-à-vis an example posed by Bernstein. It is argued that the only reasonable extension of Reichenbach's principle stands in conflict with a recent proposal due to Horwich. I also discuss prospects of the principle of the common cause in the light of these and other difficulties known in the literature and argue that a more viable version of the principle is the one provided by Penrose and Percival (1962).