Elemental causal induction 1 Running head: ELEMENTAL CAUSAL INDUCTION Elemental causal induction

We present a framework for the rational analysis of elemental causal induction – learning about the existence of a relationship between a single cause and effect – based upon causal graphical models. This framework makes precise the intuitive distinction between causal structure and causal strength: the difference between asking whether or not a causal relationship exists, and asking how strong that causal relationship might be. We show that the two leading rational models of elemental causal induction, ∆P and causal power, both estimate causal strength, and introduce a new rational model, causal support, that assesses causal structure. Causal support provides a better account of a large number of existing datasets than either ∆P or causal power. It also predicts several phenomena that cannot be accounted for by other models, which we explore through a series of experiments. These phenomena include the complex interaction between ∆P and the base-rate probability of the effect in the absence of the cause, sample size effects, inferences from incomplete contingency tables, and causal learning from rates. Elemental causal induction 3 Elemental causal induction The contagion spread rapidly and before its progress could be arrested, sixteen persons were affected of which two died. Of these sixteen, eight were under my care. On this occasion I used for the first time the affusion of cold water, in the manner described by Dr. Wright. It was first tried in two cases. . . The effects corresponded exactly with those mentioned by him to have occurred in his own case and thus encouraged the remedy was employed in five other cases. It was repeated daily, and of these seven patients, the whole recovered. James Currie (1798/1960, p. 430)