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