Generalised Reichenbachian common cause systems

The principle of the common cause claims that if an improbable coincidence has occurred, there must exist a common cause. This is generally taken to mean that positive correlations between non-causally related events should disappear when conditioning on the action of some underlying common cause. The extended interpretation of the principle, by contrast, urges that common causes should be called for in order to explain positive deviations between the estimated correlation of two events and the expected value of their correlation. The aim of this paper is to provide the extended reading of the principle with a general probabilistic model, capturing the simultaneous action of a system of multiple common causes. To this end, two distinct models are elaborated, and the necessary and sufficient conditions for their existence are determined.

     

Correlations, deviations and expectations: the Extended Principle of the Common Cause

The Principle of the Common Cause is usually understood to provide causal explanations for probabilistic correlations obtaining between causally unrelated events. In this study, an extended interpretation of the principle is proposed, according to which common causes should be invoked to explain positive correlations whose values depart from the ones that one would expect to obtain in accordance to her probabilistic expectations. In addition, a probabilistic model for common causes is tailored which satisfies the generalized version of the principle, at the same time including the standard conjunctive-fork model as a special case.