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The principle of common cause asserts that positive correlations betweencausally unrelated events ought to be explained through the action of someshared causal factors. Reichenbachian common cause systems are probabilisticstructures aimed at accounting for cases where correlations of the aforesaidsort cannot be explained through the action of a single common cause. Theexistence of Reichenbachian common cause systems of arbitrary finite size foreach pair of non-causally correlated events was allegedly demonstrated byHofer-Szab\'o and R\'edei in 2006. This paper shows that their proof islogically deficient, and we propose an improved proof.

Do Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist?