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

Abstract

The Principle of the Common Cause is usually understood to provide causal explanations for probabilistic correlations obtaining between causally unrelated events. In this work, 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.

Simulating daily field crop canopy photosynthesis: an integrated software package

“…First, Propositions 4 and 6 both rectify the results announced in Mazzola (2013), where it was implicitly assumed that expected correlations should be greater than or equal to zero. This led to the erroneous claim that a generalised common cause should exist, in some extension of the initial probability space, for every positive deviation.…”

“…In Mazzola (2013), however, I argued that Reichenbach's treatment is overly restrictive, as it rests on a too narrow conception of improbable coincidences, and on a correspondingly narrow understanding of the explanatory function of common causes. I accordingly proposed an improved interpretation of the principle, along with a suitably revised probabilistic model for common causes, which generalises Reichenbach's original model in two respects.…”

“…Nevertheless, there is one respect in which the probabilistic model proposed in Mazzola (2013) is still not general enough. Like Reichenbach's original account, in fact, it depicts the action of a single common cause, and it is accordingly inadequate to capture instances whereby two coordinated effects are brought about by a system of distinct common causes.…”

“…Firstly, in Sect. 2 the extended interpretation of the principle elaborated in Mazzola (2013) will be briefly outlined, and given formal treatment. Next, in Sect.…”

Generalised Reichenbachian common cause systems

“…Two final remarks may be added at this at this point. First, Proposition 4 and Proposition 6 both rectify the results announced in [11], where it was implicitly assumed that expected correlations be greater than or equal to zero, leading to the erroneous claim that a generalised common cause should exist, in some extension of the initial probability space, for every positive deviation. Second, GHR-RCCSs and GM-RCCSs for a given deviation may not coexist in the same probability space.…”