Assessing interactive causal influence.

The discovery of conjunctive causes—factors that act in concert to produce or prevent an effect— has been explained by purely covariational theories. Such theories assume that concomitant variations in observable events directly license causal inferences, without postulating the existence of unobservable causal relations. This article discusses problems with these theories, proposes a causal-power theory that overcomes the problems, and reports empirical evidence favoring the new theory. Unlike earlier models, the new theory derives (a) the conditions under which covariation implies conjunctive causation and (b) functions relating observable events to unobservable conjunctive causal strength. This psychological theory, which concerns simple cases involving 2 binary candidate causes and a binary effect, raises questions about normative statistics for testing causal hypotheses regarding categorical data resulting from discrete variables. A single causal factor is often perceived as contributing toward producing an effect yet insufficient to produce it on its own. Low body resistance in the absence of a flu virus is not by itself sufficient to cause one to have the flu; neither, typically, is the presence of a flu virus per se. The two in conjunction, however, often do cause one to come down with the flu. Likewise, striking a match per se does not cause it to light—there must be oxygen in the environment, the match must be combustible, and so forth. Cigarette smoke per se does not cause lung cancer—the smoke must be inhaled over a relatively long interval, the smoker must be susceptible to the disease, and so forth. The susceptibility itself is probably in turn specified by multiple genetic factors. Hard work alone typically does not produce success; it must be combined with talent and opportunity. Most causes in the real world, like these examples, are complex, involving a conjunction of factors acting in concert, rather than simple, involving a single factor acting alone. How do reasoners come to know that there is something special about the conjunction of several factors such that it can produce or prevent an effect? We first present some phenomena that are inexplicable by previous psychological accounts of conjunctive causation. To explain these phenomena, as well as to solve other problems that beset previous accounts, we propose our causal-power theory of the assessment of interactive causal influence. We then review previous findings in the literature in light of our new theory and report new empirical evidence in support of the theory. Finally, we discuss some implications of our approach for the normative testing of causal hypotheses regarding data resulting from discrete variables. Our new theory, like many previous psychological accounts of conjunctive causation (Cheng & Novick, 1990, 1992; Forsterling, 1989; Hewstone & Jaspars, 1987; Hilton & Slugoski, 1986; Kelley, 1967), is covariational in that it bases causal inferences on concomitant variations in observed events as well as on other observable features such as temporal ordering. Previous accounts, however, are purely covariational in that they do not consider the possible existence of unobservable causal structures to arrive at their output. In contrast, our theory explicitly incorporates into its inference procedure the possible existence of distal causal structures: Structures in the world that exist independently of one’s observations. More specifically, in our theory we hypothesized that reasoners estimate the theoretical probability with which candidate causes both individually and in conjunction influence the effect in question, by producing it or preventing it. We call this theoretical probability the causal power of the (simple or conjunctive) candidate (after Cartwright, 1989). Our new approach allowed us to derive the conditions under which observed covariation implies conjunctive causation as well as the functions relating covariation to conjunctive causal power.