Coherent Generalization Across Contexts

Two competing psychological approaches to causal learning make different predictions regarding what aspect of perceived causality is generalized across contexts. Two experiments tested these predictions. In one experiment, the task required a judgment regarding the existence of a simple causal relation; in the other, the task required a judgment regarding the existence of an interaction between a candidate cause and unobserved background causes. The task materials did not mention assessments of causal strength. Results indicate that causal power (Cartwright, 1989; Cheng, 1997) is the mental construct that people carry from one context to another. Judgments about cause-and-effect relations occur in contexts that are like rivers—one never steps into the same context twice. Generalization from one context to another is therefore paramount. In fact, generalizing from the learning context to whatever new context may come is the raison d’être of causal learning. What is it that a reasoner carries from one situation into another? Let us formulate this question more specifically in terms of the scenarios illustrated in Figure 1. Imagine that you are presented with data from two studies, conducted in different laboratories, that tested the influence of two allergy medicines on headache (a possible side effect). In each study, allergy patients were randomly assigned to two groups: a treatment group and a no-treatment (i.e., control) group. In the first study (Fig. 1a), Medicine A alone was administered. In the second (Fig. 1b), Medicines A and B were administered in combination. Headache (indicated by a frowning face, as opposed to a smiling face) occurred with a different frequency in each of the four groups. What is your best bet, based on the results from both studies, regarding whether or not Medicine B causes headache? Presumably, if you perceive a ‘‘change’’ in the results across treatments (i.e., Medicine A in one study and both medicines in the other), you might attribute this change to the introduction of Medicine B in the second study. But what constitutes a ‘‘change’’? To put the question another way, what is assumed to be invariant, and hence to generalize, across contexts? Although the target question in this scenario concerns Medicine B, the psychological representation of interest concerns Medicine A, the medicine that occurs in both contexts. One could ask a direct question about the generalization of Medicine A across contexts. The very wording of a direct question, however, might bias the answer toward one model or another (for a discussion of the striking influence of wording of causal questions on responses, see Buehner, Cheng, & Clifford, 2003). Introducing Medicine B into the scenario and letting it be the target of the question allows one to assess implicitly and without bias what perceived aspect of Medicine A generalizes across contexts. In the rest of this article, we briefly review two approaches to causal learning and present two experiments that tested hypotheses about generalization across contexts, making use of scenarios such as those in Figure 1. CAUSALVERSUS PURELY COVARIATIONAL ACCOUNTS OF CAUSAL LEARNING Causal relations encapsulate how the world works. A classic problem in the field of artificial intelligence is the frame problem (McCarthy & Hayes, 1969): Given the vast amount of empirical information that is available at each moment in each situation, which kinds of information are the most relevant across time and contexts and therefore should be selected for representation? A prevailing answer is: causal relations (e.g., Pearl, 2000; Spirtes, Glymour, & Scheines, 1993/2000). Concurrently in psychology, causal learning has emerged as an important topic (e.g., Blaisdell, Sawa, Leising, & Waldmann, 2006; Dickinson, Shanks, & Evenden, 1984; Glymour, 2001; Griffiths & Tenenbaum, 2005; Waldmann & Holyoak, 1992). The two dominant approaches to causal learning—the causal approach (e.g., Cheng, 1997) and the purely covariational approach (e.g., Rescorla & Wagner, 1972)—make precise and fundamentally different Address correspondence to Mimi Liljeholm, Department of Psychology, Franz Hall, University of California, Los Angeles, CA 90095-1563, e-mail: [email protected]. PSYCHOLOGICAL SCIENCE 1014 Volume 18—Number 11 Copyright r 2007 Association for Psychological Science predictions regarding what remains invariant across contexts (Cheng, 2000; Cheng, Novick, Liljeholm, & Ford, 2007). At the heart of the debate between these approaches is the issue of whether or not reasoners make (tacit) generic assumptions about causal events in the distal world, events that (as Hume, 1739/ 1987, noted) are unobservable. Assumptions about unobservable events, ceteris paribus, are understandably objectionable. In this article, we argue that the payoff of such assumptions is the capability of making coherent generalizations across contexts. Although some studies have investigated generalization to novel causal contexts (e.g., Lien & Cheng, 2000; Povinelli, 2000), none have tested the distinct predictions of the two approaches. The experiments reported here tested these predictions. DP and Causal Power: Two Psychological Accounts of Causal-Strength Estimation Purely covariational models of causal learning attempt to sidestep assumptions regarding unobservable distal events. According to a well-established model of covariation, the DP rule (Jenkins & Ward, 1965), adapted to apply to subsets of events in which causes other than the candidate cause remain constant (Cheng & Holyoak, 1995), reasoners contrast two probabilities: P(e|c), the probability of a target effect e given the presence of a candidate cause c, and P(e| c), the probability of e given the absence of c: DPc 1⁄4 Pðe j cÞ Pðe j cÞ ð1Þ These conditional probabilities are directly estimable by the observable relative frequencies of the relevant events. Both e and c are binary variables. Depending on whether DP is greater than, less than, or not noticeably different from 0, c is assumed to be a generative cause, preventive cause, or noncause of e, respectively. Under a set of conditions in which learning is at asymptote, the DP rule is equivalent to Rescorla and Wagner’s model (1972; see Danks, 2003), and both accounts have been adopted to model causal strength (e.g., Spellman, 1996). For all conditions in our experiments, these accounts make the same ordinal predictions. Fig. 1. Illustration of two hypothetical studies testing the influences of Medicines A and B on headache. The illustrations at the top show patients who were not exposed to any medicine; the bottom illustrations show patients who were exposed to either (a) Medicine A alone or (b) Medicines A and B in combination. In these studies, the causal power of the treatment (an estimate of a distal property) remains constant across studies while DP (a proximal property) varies. Values of Rescorla and Wagner’s (1972) model (RW) and of the causal-support model (Griffiths & Tenenbaum, 2005) are also listed. Values of causal support were generated with a noisy-OR function (see the section on Independent Causal Influence). Volume 18—Number 11 1015 Mimi Liljeholm and Patricia W. Cheng