Close Does Count: Evidence of a Proximity Effect in Inference from Causal Knowledge

Close Does Count: Evidence of a Proximity Effect in Inference from Causal Knowledge Russell C. Burnett (rburnett@mscc.huji.ac.il) School of Education, The Hebrew University of Jerusalem Jerusalem 91905, Israel years been applied to the psychology of learning complex causal systems (e.g., Gopnik et al., 2004; Steyvers, Tenenbaum, Wagenmakers, & Blum, 2003). The central principle in this framework is known as the causal Markov condition, and it can be interpreted as saying just when variables in causal systems are relevant to one another and when they are not. Formally, the causal Markov condition says that a variable is independent of all variables that are not its descendants in causal structure, conditional on its immediate cause(s). For the current example, this means that liver damage is independent of virus X (a nondescendant in causal structure) if the presence/absence of the enzyme deficiency (the immediate cause of liver damage) is known. Since it is known whether the patient has the enzyme deficiency, the presence or absence of virus X is irrelevant to an inference about liver damage. This kind of conditional independence—independence of two variables just when the state of a third is known—is often called “screening off. ” We say, for example, that virus X is screened off from liver damage by the enzyme deficiency. Indirectly related variables in causal chains are screened off from one another by mediating variables, but this is not the only form that screening off can take. For instance, the causal Markov condition also implies that variables with a single common cause are screened off from one another by that cause. To modify the current example, if it were known that virus X causes, by separate mechanisms, both the enzyme deficiency and liver damage, then enzyme deficiency would be irrelevant to an inference about liver damage given information about the virus. This form of screening off—screening off by a common cause—was described by Reichenbach (1956). Rehder and Burnett (2005) asked participants to draw inferences like the ones just described and found that greatest relevance was indeed assigned to variables deemed relevant by the causal Markov condition. However, inferences were also influenced by variables that, according to the causal Markov condition, should have been screened off from the variable about which inferences were being made. This was found for causal systems with several different structures, including the chain and common-cause structures. When making inferences about a variable in a chain, participants implicitly assigned relevance to indirectly related variables even when the state of a mediating variable was known. When making inferences about one of multiple effects of a single cause, participants assigned relevance to the other effects even when the state of the common cause was known (for a related finding see Walsh & Sloman, 2004). This phenomenon was termed nonindependence, since relevance was assigned in violation Abstract Two studies are reported in which participants drew inferences about variables in systems of causal relationships. Previous work has shown that such inferences are influenced by information about variables that, on a normative account of causal reasoning, should be irrelevant. The present studies tested two hypotheses about how relevance is assigned to these normatively irrelevant variables. Though results were mixed, they suggest that greater relevance is assigned to variables that are closer in known causal structure to the variable about which an inference is being made. Though the learning of causal relationships from correlational evidence has received a fair amount of attention from psychologists, the use of causal knowledge to make inferences and predictions has not. This may be due to the fact that until recently most studies have focused on how learners detect the existence or strength of a causal relationship between just two dichotomous variables: a single cause and a single effect, each either present or absent. Drawing inferences or predictions from knowledge of a single causal relationship is presumably straightforward in the sense that each variable is predictive of the other: An effect is more likely present when its cause is present, and vice versa. This paper deals with inferences about variables in complex causal systems, that is, systems of causal relationships among three or more variables. Such inferences are often less straightforward than inferences from single causal relationships, in that it is not always so clear whether or under what conditions variables are relevant to one another. Suppose, for example, that a doctor knows that virus X causes a certain enzyme deficiency, which in turn causes liver damage. That is, the doctor knows this three-variable causal chain: virus X enzyme deficiency liver damage . Suppose this doctor sees a patient for whom both the presence or absence of the virus and the presence or absence of the enzyme deficiency are known, and the doctor must make an inference about whether this patient is at risk for liver damage. In this case virus X and enzyme deficiency can be called observed variables, and liver damage an unobserved variable. To what extent would (or should) information about each of the two observed variables influence the doctor’s inference? Previous work suggests that such inferences are partly but not fully explained by a normative or rational theoretical framework, variously known as causal Bayesian network theory or graphical causal model theory (Pearl, 2000; Spirtes, Glymour, & Scheines, 2000), which has in recent