From covariation to causation: A causal power theory
Because causal relations are neither observable nor deducible, they must be induced from observable events. The 2 dominant approaches to the psychology of causal induction-the covariation approach and the causal power approach-are each crippled by fundamental problems. This article proposes an integration of these approaches thai overcomes these problems. The proposal is that reasoners innately treat the relation between covariation (a function denned in terms of observable events) and causal
... vents) and causal power (an unobservable entity) as that between scientists' law or model and their theory explaining the model. This solution is formalized in the power PC theory, a causal power theory of the probabilistic contrast model (P. W. Cheng & L. R. Novick, 1990) . The article reviews diverse old and new empirical tests discriminating this theory from previous models, none of which is justified by a theory. The results uniquely support the power PC theory. How does a reasoner come to know that one thing causes another? Psychological work on this issue of causal induction has been dominated by two basic approaches that have generally been regarded as opposing each other. One of these, the covariation approach, traces its roots to David Hume (1739/1987). This approach is motivated by the problem that the reasoners' sensory input-the ultimate source of all information that they have-does not explicitly contain causal relations. It follows that acquired causal relations must be computed from the sensory input in some way. One's sensory input clearly yields such information as the presence and absence of a candidate cause and of the effect, as well as the temporal and spatial relations between them. Treating such "observable" information as the input to the process of causal induction, models under this approach attempt in some way to assess covariation between a candidate cause and the effect (i.e., the extent to which the two vary together). An influential model of covariation-often called the contingency model-was proposed by researchers across various disciplines Rescorla, 1968; Salmon, 1965) . Interpreting this model in causal terms, AP" the contingency between candidate cause i and effect e is defined by AP, = P(e\i) -P(e\T>, (1) may be sent via Internet to firstname.lastname@example.org. where P(e \ i) is the probability of e given the presence of i and P(e | J) is that probability given the absence of i. (The conditional probabilities in the equation are estimated by the respective relative frequency of events for which e occurs in the presence and in the absence of i.) If AP, is noticeably positive, i is a generative or facilitatory cause, and, if it is noticeably negative, i is an inhibitory or preventive cause. Otherwise, i is noncausal. In the psychological literature, the Humean approach has split into several subdivisions. Statistical contingency models based on the AP rule have been contrasted with various types of associative models, in particular Rescorla and Wagner's (1972) discrepancy-based predictive learning rule (e.g.. It is important to emphasize, however, that all covariation models of causality face a major common hurdle: As many have noted, covariation does not always imply causation. AP is clearly insufficient as a criterion for causal induction, because not all covariational relations are perceived as causal. Many things follow one another regularly, yet one does not infer a causal relation between them. Sunrise might occur every day after a rooster on a farm crows (but sunrise does not occur at other times during the day when the rooster does not crow), and one class for a student might routinely follow another (but if the first class does not meet, for example during a holiday, neither does the second). Yet one would not infer that the rooster's crowing causes the sun to rise or that one class causes another. None of the subtypes of covariation models, as I show later, have provided an account 367 368 CHENG 1 Kant (1781/1965), in fact, argued that people have general, but not specific, a priori knowledge about causality. He wrote, "certainly, empirical laws, as such, can never derive their origin from pure understanding" (p. 148) and to "obtain any knowledge whatsoever of these special laws, we must resort to experience" (p. 173).