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The Relationship Between Children’s Causal and Counterfactual Judgments

Teresa McCormack Caren Frosch

Queen’s University Belfast

Patrick Burns

University of Birmingham

As should be clear from the contributions to this volume by philosophers, there is a long tradition of philosophical accounts of causation that link causal and counterfactual claims (Collins, Hall, & Paul, 2004; Hart & Honoré, 1985; Lewis, 1973). Put simply, the basic idea is that what it means to say that C causes E is not just to say that if C occurs, E will occur, but also to say that if C were not to occur, E would not occur. Various accounts finesse this general claim in considerable detail (see Collins et al., 2004); the most recent influential related theory is that of Woodward (2003, 2007, this volume). As Woodward points out, most philosophical accounts are “intended as accounts about the world, rather than accounts of anyone’s psychology” (2007, p. 25). Nevertheless, it may be a worthwhile psychological project to explore the extent to which such theories can inform descriptive accounts of how causal learning and cognition actually function.

From a psychological perspective, we can make a simple distinction between two possible ways in which counterfactual and causal reasoning might be related. The first, which we will call the counterfactual process view, is that counterfactual thought is typically a necessary part of the processing involved in making causal judgments. The alternative possibility is what we will call the psychological relatedness view: that counterfactual judgments are closely related psychologically to counterfactual judgments insofar as (1) the ability to make a causal judgment is usually accompanied by the ability to make the appropriate counterfactual judgment and vice-versa, and (2) at least under some circumstances counterfactual and causal judgments are consistent with each other. On the psychological relatedness view, however, counterfactual cognition may not necessarily play a role in the process of reaching causal conclusions. The aim of this chapter is to consider how these viewpoints have influenced research by developmental psychologists, and to discuss whether our own experimental studies provide evidence in support of either of these approaches.

Psychological process view

For developmental psychologists, the most familiar version of a process view comes from Harris, German, and Mills’s (1996) influential paper, in which they argued that counterfactual thought may play a central role in children’s causal judgments. In this paper, they drew heavily on analyses from the philosophical literature that closely link counterfactual and causal claims, in particular that of Mackie (1974). One of the aims of Harris et al.’s paper was to demonstrate that young preschoolers can not only make counterfactual judgments when asked to do so, but will spontaneously invoke counterfactual alternatives to events in situations in which they are asked to explain why certain outcomes had occurred or when asked how such outcomes could have been prevented. Harris et al. (1996) concluded that it is likely that children’s causal interpretations of events are typically informed by a consideration of counterfactual alternatives, and that this could be the case from very early in development.

The findings of recent research with adults have brought into question the notion that causal judgments are frequently underpinned by a consideration of counterfactual alternatives (for review, see Mandel, this volume). Furthermore, there is considerable debate over whether Harris et al. (1996) convincingly demonstrated that preschoolers are capable of genuinely counterfactual thought (see contributions by Beck, Riggs, & Burns, and by RafetsederPerner to this volume). It is fair to say that Harris’s suggestion that children’s causal judgments are typically arrived at by a process of considering counterfactual alternatives has not been widely adopted by developmentalists. Nevertheless,we can still think about whether it is possible to identify any circumstances in which children’s causal judgments might plausibly recruit counterfactual reasoning.In the final section of this chapter, we discuss one possible circumstance in which children may draw conclusions based on counterfactual reasoning, and outline some initial experimental evidence that supports this suggestion. However, we first turn to a consideration of the alternative claim that we have termed a psychological relatedness view: that counterfactual judgments are closely related to causal judgments.

Psychological relatedness views

One of the most influential recent accounts of causal learning that can be interpreted as a psychological relatedness view has been put forward by the developmental psychologist Alison Gopnik. The causal Bayes net approach espoused by Gopnik and colleagues (e.g., Gopnik et al., 2004; Gopnik, Sobel, Schulz, & Glymour, 2001; Sobel, Tenenbaum, & Gopnik, 2004), has not only generated consider debate about the nature of causal learning, but has also provided a new context in which the relationship between causal and counterfactual cognition can be considered. This account is a version of the causal models approach to causal learning (Sloman, 2005), since it assumes that both children and adults operate with models of structure of the causal relationships between variables, rather than simply, for example, learning associations between them. On the causal Bayes net approach, these models are assumed to essentially represent patterns of conditional probabilities between variables, and are constructed and updated in a way that obeys Bayesian principles. For present purposes, it is not necessary to describe the details of such principles (see various contributions to Gopnik & Schulz, 2007, for reviews). Rather, the key relevant assumption of this approach is that such models can be used to predict the effects of hypothetical interventions on (i.e., manipulations to the values of) variables within a given model. In other words, the claim is that such models allow systematic predictions to be made about the likely outcome of altering certain aspects of the world. Because of this property, it has been argued that these inferential structuresnot only support causal judgments but can also be used to generate counterfactual predictions (Gopnik & Schultz, 2007; see also Hagmayer, Sloman, Lagnado, & Waldmann, 2007; Sloman & Lagnado, 2005). As Hagmayer et al. describe, doing this would require constructing an initial model of the causal relationships between aspects of the world on the basis of observation, and then performing an imaginary selective intervention on the relevant variable within the previously-constructed model. Given certain assumptions about the nature of the represented relationships between the variables in the model (in particular, that they are genuinely causal relationships rather than simply probabilistic ones), accurate counterfactual prediction should be possible. Thus, the causal Bayes net framework seems to readily yield an interpretation in terms of what we have called a psychological relatedness approach.

Thus, this general approach makes a clear empirical prediction: if participants have extracted a causal model on the basis of their observations of variables, they should be able to make appropriate counterfactual predictions. To illustrate, consider a situation in which a participant is asked to make counterfactual predictions about the effects of intervening on a variable after extracting either a common cause causal model or a causal chain modelof the relationships between three variables (see Figure 1). In a common cause model, variable A is represented as the common single cause of B and C, whereas in a causal chain model, A is represented as causing an intervening event B which then causes a final effect C. A crucial difference between these models is what they should predict about the effect of making a hypothetical intervention on variable B. For example, other things being held constant, preventing B from occurring should have no effect on whether C occurs following A under a common cause model, whereas under a causal chain model, C should not be able to occur if B is prevented from occurring. Thus, this type of account assumes that participants should vary their predictions about the effects of preventing the occurrence of B depending on whether they have been given observations that lead them to extract a causal chain versus a common cause model. Below, we discuss some of our experimental studies that have examined whether or not this is the case in children.

We note that Gopnik and colleagues do not in their writingsassume that a process account of causal judgment holds (i.e., that causal conclusions are typically reached by a process of considering counterfactual alternatives). Indeed, Schulz et al. (2007) accept that children can acquire causal knowledge by many routes. However, at least in some writings, it would appear that they intend their account to go further than the claim that causal representations should support counterfactual judgments. Specifically, influenced by the interventionist approach to causation in philosophy (Woodward, 2003, 2007, this volume), Schulz et al. (2007) suggest that causal knowledge is in fact essentially knowledge about the effects of observed, hypothetical, or counterfactual interventions. That is, roughly speaking, what it is to represent A as the cause of B just is a matter of be committed to the idea that intervening on or manipulating the value of A will affect B. They contrast such an approach with more widely accepted approaches with developmental psychology that characterize causal knowledge in terms of the knowledge about mechanism (e.g., most notably, that of Shultz, 1982; but see also Schlottmann, 1999, 2000; White, 1995). Although Schulz et al. acknowledge that children may possess knowledge about the operation of specific mechanisms that they have encountered, such mechanism knowledge is not thought to be basic to representations of causal relationships. Thus, Schulz et al. argue that “a causal relation is defined… in terms of the real and counterfactual interventions it supports” (p. 69), and that “when children infer that a relationship is causal, they commit to the idea that certain patterns of interventions and outcomes will hold” (p. 70). Our experimental studies examined whether this is indeed the case.

The consistency of children’s causal and counterfactual judgments: causal structure judgments

In a series of studies, we have examined whether Schulz et al. (2007) are correct in suggesting that children’s judgments about the effects of counterfactual interventions should be consistent with their causal judgments. In all of these studies, we have examined scenarios in which children extract the causal structure of a three-variable system as either a causal chain or a common cause, and are then asked to make explicit judgments about the effects of intervening on one or more of the variables. In one study (Frosch, McCormack, Lagnado, & Burns, 2010), children were provided with very simple temporal cues about causal structure. Children observed a box with three differently-colored components on top of it that moved circularly on the horizontal plane, which for present purposes we can label A, B, and C. The temporal structure of the events involving A, B, and C varied between trials, and children saw a number of demonstrations of the event series in each trial.The components were spatially separated with no obvious mechanisms connecting them; in fact, unbeknownst to participants they were controlled by a computer hidden inside the apparatus. In sequential trials, A moved, followed by a short delay, then B moved, followed by an additional short delay, and then C moved. In this condition, children as young as 5 years judged that A, B, and C formed a causal chain, by selecting an appropriate diagram to match their model choice. Following Schulz, Gopnik, and Glymour (2007), these diagrams were in the form of anthropomorphized pictures in which hands reaching from one component to another signified a causal link (see Figure 2a for an example; the particular objects used as A, B, and C varied between trials). In synchronous trials, A moved, and then after a short delay B and C moved simultaneously. In these trials, 5-year-olds reliably judged that A was a common cause of B and C (see Figure 2b for an example). After children had selected their model choices, we placed the diagram of the model in front of them so that they could remember what causal structure they had selected. Given that the only difference between the sequences that children observed across trial types was the temporal arrangement of the events, we can be confident that the cross-trial differences in children’s causal structure judgments were a result of these judgments being based on the simple temporal cues provided.

After children had made their causal structure judgments, we then asked them specific counterfactual questions, the answers to which should have differed across the trial types. Children were asked what would have happened during the previous demonstrations of the box’s operation if B or C had been unable to operate. More specifically,they were asked whether C would have moved if B had been unable to operate, and whether B would have moved if C had been unable to operate. We showed children how individual components could have been disabled (described to children as“stopped from working”) using a small vertical bar (fashioned as a “Stop” sign) that prevented a component from moving. If children were correctly using the causal models that they had extracted to make counterfactual judgments, their answers to these questions should have differed appropriately across trial types (see Table 1 for correct answers for each model). In particular, when children had judged the structure to be a causal chain structure, they should have predicted that C would not have moved if B had been stopped from working. However, this was not the case. Children’s counterfactual judgments had low consistency with their causal model choices, and did not differ significantly across trial types. This was true for older children (6-7-year-olds) as well as 5-year-olds, making it unlikely that children’s difficulties stemmed from understanding the counterfactual questions. Thus, the findings of this study do not support the suggestion that children’s representations of causal structure support counterfactual judgments about interventions appropriately.

Although we do not believe that children’s difficulties stemmed from understanding the counterfactual questions that we posed, evidence from some developmental studies (e.g., Perner, Sprung, & Steinkogler, 2004; Riggs, Peterson, Robinson, & Mitchell, 1998) suggests that young children may find questions posed as future hypotheticals (questions of the form “what will happen”) somewhat easier than counterfactual questions (questions of the form “what would have happened ”). This issue is discussed in Rafetseder and Perner’s contribution to this volume. Indeed, Woodward (this volume) argues that an interventionist account of causal cognition need only assume that causal representations support judgments about future hypothetical circumstances, rather than those psychologists would usually consider to be counterfactual. In another study (Burns & McCormack, 2009) we used a similar procedure, with children extracting causal structure based on temporal cues for three variables ABC, again as either causal chain or common cause structures. Children were asked sets of causal questions (“which one made B go?) and also asked to choose a diagram that reflected their causal judgments. Following these judgments, children were asked to make judgments about interventions: the experimenter carried out the intervention by physically preventing either component B or C from operating, and then asked children a future hypothetical question about whether the other component (B or C) would operate when the event sequence was initiated. In this study, children were shown only a single trial type to ensure that their answers were not affected by observing other causal structures. Even under these circumstances, 6-7-year-olds’ judgments about interventions were not consistent with their causal model judgments. Adults were tested as well, and we found that their intervention judgments were consistent with their causal model judgments, and varied appropriate across trial types.

One possible explanation of these findings is that the judgments children have to make have two components, insofar as they involve inferring the consequences of (i) preventing one event (B or C) from occurring and then (ii) the subsequent generation of the overall event sequence by initiating event A. We label such interventions as prevent-then-generate interventions, because of the requirement to infer the consequences of both of these components. Arguably, such interventions are potentially more complex to reason about than interventions that simply involve inferring the consequences of manipulating a single component (e.g., what would happen if B or C themselves were manipulated?), which we refer to as simple generative intervention judgments. In a further study, children were asked to make a more simple intervention judgment: after they had selected their causal model they were asked a future hypothetical question about what would happen to either B or C if the other component were made to move [e.g., “if I move (B) like this, will (C) go?”]. Again, 6-7-year-olds’ answers to these more simple generative intervention questions were not consistent with their causal structure judgments and did not differ appropriately across trial types.

Thus, across a series of studies we did not find support for Schulz et al.’s (2007) claim that “when children infer that a relationship is causal, they commit to the idea that certain patterns of interventions and outcomes will hold” (p. 70). Although children inferred that they were observing different causal structures across the two trial types, their counterfactual and future hypothetical judgments about the effects of interventions were not consistent with these inferences. The causal structures that we used were very simple, and indeed they were chosen because they are generally considered to be the building blocks of more complex causal structures (along with a three-variable common effect model; Hagmayer et al., 2007). However, we note that our findings are potentially inconsistent with those of Schulz, Gopnik, and Glymour (2007; Exp. 2). In their study, children were told that a system of two gears had a particular causal structure, illustrated using diagrams similar to those that we used. They then asked children whether each one of the gears would move when the other one was removed. They found that, across four different causal structures, children answered these questions correctly more frequently than would have been expected by chance. We note, though, that although performance was above chance, in no instance did the majority of children give the correct answers to these hypothetical questions (i.e., no more than 8 out of their sample of 16 children answered the questions correctly for any given causal structure). Nevertheless, the authors argue that the findings suggest that children can use their causal structure knowledge to make predictions about the effects of interventions. There are a large number of differences between our methodology and that of Schulz et al. (2007), including the physics of the apparatus and the number of moving components (e.g., they used two interlocking gears whereas we used three spatially distinct components). Here we focus on just one difference that may potentially be important: Whereasin our studies children were given temporal cues to derive causal structure, Schulz et al. (Exp. 2) simply told children what the causal structure was.