The Invisible Hand: Toddlers Connect Probabilistic Events With Agentive Causes

Children posit unobserved causes when events appear to occur spontaneously (e.g., Gelman & Gottfried, 1996). What about when events appear to occur probabilistically? Here toddlers (M = 20.1 months) saw arbitrary causal relationships (Cause A generated Effect A; Cause B generated Effect B) in a fixed, alternating order. The relationships were then changed in one of two ways. In the Deterministic condition, the event order changed (Event B preceded Event A); in the Probabilistic condition, the causal relationships changed (Cause A generated Effect B; Cause B generated Effect A). As intended, toddlers looked equally long at both changes (Experiment 1). We then introduced a previously unseen candidate cause. Toddlers looked longer at the appearance of a hand (Experiment 2) and novel agent (Experiment 3) in the Deterministic than the Probabilistic conditions, but looked equally long at novel non‐agents (Experiment 4), suggesting that by 2 years of age, toddlers connect probabilistic events with unobserved agents.     

Effect of grouping of evidence types on learning about interactions between observed and unobserved causes

When a cause interacts with unobserved factors to produce an effect, the contingency between the observed cause and effect cannot be taken at face value to infer causality. Yet it would be computationally intractable to consider all possible unobserved, interacting factors. Nonetheless, 6 experiments found that people can learn about an unobserved cause participating in an interaction with an observed cause when the unobserved cause is stable over time. Participants observed periods in which a cause and effect were associated followed by periods of the opposite association ("grouped condition"). Rather than concluding a complete lack of causality, participants inferred that the observed cause does influence the effect (Experiment 1), and they gave higher causal strength estimates when there were longer periods during which the observed cause appeared to influence the effect (Experiment 2). Consistent with these results, when the trials were grouped, participants inferred that the observed cause interacted with an unobserved cause (Experiments 3 and 4). Indeed, participants could even make precise predictions about the pattern of interaction (Experiments 5 and 6). Implications for theories of causal reasoning are discussed.     

Valuing intervention and observation

Understanding causal relations is fundamental to effective action but causal data can be confounded. We examined the value that participants placed on data derived from a hypothetical intervention or observation. Our materials involved a possible cause (“bottled water”), a possible confound (“food”), and a context (“a restaurant”). We supposed that participants seek to draw as specific a causal inference as possible from presented data and value information sources more highly that allow them to do so. On this basis, we predicted that in circumstances where an intervention removed the confounding causal factor but observation did not, participants would prefer data derived from an intervention when the possible cause was present (the bottled water was drunk) but show the reverse preference when the possible cause was absent (the bottled water was not drunk). Experiment 1 confirmed this prediction. Using a between-subjects design, Experiment 2 tested for a difference in confidence in causal judgements given identical data, including data on the confound, as a function of method of data collection (intervention or observation). There was no significant difference in confidence ratings between the two methods but confidence ratings were sensitive to the probability of an effect (illness) given the cause. Using a within-subjects design, Experiment 3 revealed systematic individual differences in preference for the two methods. Participants were divided between those who considered intervention more confounded and those who considered observation more confounded. Our experiments point to the subtleties of participants' evaluation of data from studies of human beings.     

Are Causal Structure and Intervention Judgments Inextricably Linked? A Developmental Study

The application of the formal framework of causal Bayesian Networks to children’s causal learning provides the motivation to examine the link between judgments about the causal structure of a system, and the ability to make inferences about interventions on components of the system. Three experiments examined whether children are able to make correct inferences about interventions on different causal structures. The first two experiments examined whether children’s causal structure and intervention judgments were consistent with one another. In Experiment 1, children aged between 4 and 8 years made causal structure judgments on a three‐component causal system followed by counterfactual intervention judgments. In Experiment 2, children’s causal structure judgments were followed by intervention judgments phrased as future hypotheticals. In Experiment 3, we explicitly told children what the correct causal structure was and asked them to make intervention judgments. The results of the three experiments suggest that the representations that support causal structure judgments do not easily support simple judgments about interventions in children. We discuss our findings in light of strong interventionist claims that the two types of judgments should be closely linked.     

Effects of Causal Structure on Decisions About Where to Intervene on Causal Systems

We investigated how people design interventions to affect the outcomes of causal systems. We propose that the abstract structural properties of a causal system, in addition to people's content and mechanism knowledge, influence decisions about how to intervene. In Experiment 1, participants preferred to intervene at specific locations (immediate causes, root causes) in a causal chain regardless of which content variables occupied those positions. In Experiment 2, participants were more likely to intervene on root causes versus immediate causes when they were presented with a long‐term goal versus a short‐term goal. These results show that the structural properties of a causal system can guide the design of interventions.     

Sufficiency and Necessity Assumptions in Causal Structure Induction

Research on human causal induction has shown that people have general prior assumptions about causal strength and about how causes interact with the background. We propose that these prior assumptions about the parameters of causal systems do not only manifest themselves in estimations of causal strength or the selection of causes but also when deciding between alternative causal structures. In three experiments, we requested subjects to choose which of two observable variables was the cause and which the effect. We found strong evidence that learners have interindividually variable but intraindividually stable priors about causal parameters that express a preference for causal determinism (sufficiency or necessity; Experiment 1). These priors predict which structure subjects preferentially select. The priors can be manipulated experimentally (Experiment 2) and appear to be domain‐general (Experiment 3). Heuristic strategies of structure induction are suggested that can be viewed as simplified implementations of the priors.     

The role of preschoolers' social understanding in evaluating the informativeness of causal interventions

Preschoolers use information from interventions, namely intentional actions, to make causal inferences. We asked whether children consider some interventions to be more informative than others based on two components of an actor’s knowledge state: whether an actor possesses causal knowledge, and whether an actor is allowed to use their knowledge in a given situation. Three- and four-year-olds saw a novel toy that activated in the presence of certain objects. Two actors, one knowledgeable about the toy and one ignorant, each tried to activate the toy with an object. In Experiment 1, either the actors chose objects or the child chose for them. In Experiment 2, the actors chose objects blindfolded. Objects were always placed on the toy simultaneously, and thus were equally associated with the effect. Preschoolers’ causal inferences favored the knowledgeable actor’s object only when he was allowed to choose it (Experiment 1). Thus, children consider both personal and situational constraints on knowledge when evaluating the informativeness of causal interventions.     

Inferences about unobserved causes in human contingency learning

Estimates of the causal efficacy of an event need to take into account the possible presence and influence of other unobserved causes that might have contributed to the occurrence of the effect. Current theoretical approaches deal differently with this problem. Associative theories assume that at least one unobserved cause is always present. In contrast, causal Bayes net theories (including Power PC theory) hypothesize that unobserved causes may be present or absent. These theories generally assume independence of different causes of the same event, which greatly simplifies modelling learning and inference. In two experiments participants were requested to learn about the causal relation between a single cause and an effect by observing their co-occurrence (Experiment 1) or by actively intervening in the cause (Experiment 2). Participants' assumptions about the presence of an unobserved cause were assessed either after each learning trial or at the end of the learning phase. The results show an interesting dissociation. Whereas there was a tendency to assume interdependence of the causes in the online judgements during learning, the final judgements tended to be more in the direction of an independence assumption. Possible explanations and implications of these findings are discussed.     

Norms Affect Prospective Causal Judgments

People more frequently select norm-violating factors, relative to norm-conforming ones, as the cause of some outcome. Until recently, this abnormal-selection effect has been studied using retrospective vignette-based paradigms. We use a novel set of video stimuli to investigate this effect for prospective causal judgments—that is, judgments about the cause of some future outcome. Four experiments show that people more frequently select norm-violating factors, relative to norm-conforming ones, as the cause of some future outcome. We show that the abnormal-selection effects are not primarily explained by the perception of agency (Experiment 4). We discuss these results in relation to recent efforts to model causal judgment.     

Children’s developing understanding of the relation between variable causal efficacy and mechanistic complexity

Two experiments investigated 3–4-year-olds’ ability to infer the causal mechanisms for a pair of lights. In both experiments the exterior of the two lights appeared identical. In Experiment 1, one light displayed a stable activation pattern of a single color while the other light displayed a variable pattern of activation by cycling through a series of different colors (i.e., a more varied effect). Children were asked to judge which light had a more complex internal structure. Four-year-olds were more likely to match the light with the more variable effect with a more complex internal mechanism and the light with the more stable effect with a less complex mechanism. Three-year-olds’ responses were at chance. Experiment 2 replicated this finding when the activation patterns of the two lights were described verbally but never demonstrated. Taken together, these results suggest that 4-year-olds appreciate that the variability of an object’s causal efficacy is related to the complexity of its internal mechanistic structure.     

Children Use Temporal Cues to Learn Causal Directionality

The ability to learn the direction of causal relations is critical for understanding and acting in the world. We investigated how children learn causal directionality in situations in which the states of variables are temporally dependent (i.e., autocorrelated). In Experiment 1, children learned about causal direction by comparing the states of one variable before versus after an intervention on another variable. In Experiment 2, children reliably inferred causal directionality merely from observing how two variables change over time; they interpreted Y changing without a change in X as evidence that Y does not influence X. Both of these strategies make sense if one believes the variables to be temporally dependent. We discuss the implications of these results for interpreting previous findings. More broadly, given that many real‐world environments are characterized by temporal dependency, these results suggest strategies that children may use to learn the causal structure of their environments.     

BUCKLE: a model of unobserved cause learning

Dealing with alternative causes is necessary to avoid making inaccurate causal inferences from covariation data. However, information about alternative causes is frequently unavailable, rendering them unobserved. The current article reviews the way in which current learning models deal, or could deal, with unobserved causes. A new model of causal learning, BUCKLE (bidirectional unobserved cause learning) extends existing models of causal learning by dynamically inferring information about unobserved, alternative causes. During the course of causal learning, BUCKLE continually computes the probability that an unobserved cause is present during a given observation and then uses the results of these inferences to learn the causal strengths of the unobserved as well as observed causes. The current results demonstrate that BUCKLE provides a better explanation of people's causal learning than the existing models.     

The importance of decision making in causal learning from interventions

Recent research has focused on how interventions benefit causal learning. This research suggests that the main benefit of interventions is in the temporal and conditional probability information that interventions provide a learner. But when one generates interventions, one must also decide what interventions to generate. In three experiments, we investigated the importance of these decision demands to causal learning. Experiment 1 demonstrated that learners were better at learning causal models when they observed intervention data that they had generated, as opposed to observing data generated by another learner. Experiment 2 demonstrated the same effect between self-generated interventions and interventions learners were forced to make. Experiment 3 demonstrated that when learners observed a sequence of interventions such that the decision-making process that generated those interventions was more readily available, learning was less impaired. These data suggest that decision making may be an important part of causal learning from interventions.     

Classical conditioning mechanisms can differentiate between seeing and doing in rats

We show that the attentional-associative SLG model of classical conditioning, based on the 1996 research of Schmajuk, Lam, and Gray, correctly describes experimental results regarded as evidence of causal learning in rats: (a) interventions attenuate responding following common-cause training but do not interfere on subsequent responding during observation, and (b) interventions do not affect responding after direct-cause training or (c) causal-chain training. According to the model, responding to the weakly attended test stimulus is strongly inhibited by the intervention in the common-cause case. Instead, in the direct-cause and causal-chain cases, the strongly attended test stimulus becomes inhibitory, thereby overshadowing the inhibitory effect of interventions. Most importantly, the model predicted that with relatively few test trials (a) the 2008 results of Experiment 3 by Leising, Wong, Waldmann, and Blaisdell should be similar to those of Dwyer, Starns, and Honey's 2009 Experiment 1, showing that interventions equally affect responding after common-cause and direct-cause training; and (b) the 2006 results of Experiment 2a by Blaisdell, Sawa, Leising, and Waldmann should be similar to those of Dwyer, Starns, and Honey's 2009 Experiment 2, showing that interventions equally affect responding after common-cause and causal-chain training. When those data were made available to us, we confirmed those predictions. In agreement with the SLG associative model, but not with causal model theory, this evidence supports the notion that the attenuation of responding by interventions only following common-cause training is the consequence of well-known learning processes-latent inhibition, sensory preconditioning, conditioned inhibition, protection from extinction, and overshadowing.     

Causal status as a determinant of feature centrality

One of the major problems in categorization research is the lack of systematic ways of constraining feature weights. We propose one method of operationalizing feature centrality, a causal status hypothesis which states that a cause feature is judged to be more central than its effect feature in categorization. In Experiment 1, participants learned a novel category with three characteristic features that were causally related into a single causal chain and judged the likelihood that new objects belong to the category. Likelihood ratings for items missing the most fundamental cause were lower than those for items missing the intermediate cause, which in turn were lower than those for items missing the terminal effect. The causal status effect was also obtained in goodness-of-exemplar judgments (Experiment 2) and in free-sorting tasks (Experiment 3), but it was weaker in similarity judgments than in categorization judgments (Experiment 4). Experiment 5 shows that the size of the causal status effect is moderated by plausibility of causal relations, and Experiment 6 shows that effect features can be useful in retrieving information about unknown causes. We discuss the scope of the causal status effect and its implications for categorization research.     

Contingency bias in probability judgement may arise from ambiguity regarding additional causes

We tested whether preventive and generative reasoning processes are symmetrical by keeping the training and testing of preventive (inhibitory) and generative (excitatory) causal cues as similar as possible. In Experiment 1, we extinguished excitors and inhibitors in a blocking design, in which each extinguished cause was presented in compound with a novel cause, with the same outcome occurring following the compound and following the novel cause alone. With this novel extinction procedure, the inhibitory cues seemed more likely to lose their properties than the excitatory cues. In Experiment 2, we investigated blocking of excitatory and inhibitory causes and found similar blocking effects. Taken together, these results suggest that acquisition of excitation and inhibition is similar, but that inhibition is more liable to extinguish with our extinction procedure. In addition, we used a variable outcome, and this enabled us to test the predictions of an inferential reasoning account about what happens when the outcome level is at its minimum or maximum (De Houwer, Beckers, & Glautier, 2002). We discuss the predictions of this inferential account, Rescorla and Wagner's (1972) model, and a connectionist model—the auto-associator.     

A Process Model of Causal Reasoning

How do we make causal judgments? Many studies have demonstrated that people are capable causal reasoners, achieving success on tasks from reasoning to categorization to interventions. However, less is known about the mental processes used to achieve such sophisticated judgments. We propose a new process model—the mutation sampler—that models causal judgments as based on a sample of possible states of the causal system generated using the Metropolis–Hastings sampling algorithm. Across a diverse array of tasks and conditions encompassing over 1,700 participants, we found that our model provided a consistently closer fit to participant judgments than standard causal graphical models. In particular, we found that the biases introduced by mutation sampling accounted for people's consistent, predictable errors that the normative model by definition could not. Moreover, using a novel experimental methodology, we found that those biases appeared in the samples that participants explicitly judged to be representative of a causal system. We conclude by advocating sampling methods as plausible process-level accounts of the computations specified by the causal graphical model framework and highlight opportunities for future research to identify not just what reasoners compute when drawing causal inferences, but also how they compute it.     

The development of causal categorization

Two experiments examined the impact of causal relations between features on categorization in 5- to 6-year-old children and adults. Participants learned artificial categories containing instances with causally related features and noncausal features. They then selected the most likely category member from a series of novel test pairs. Classification patterns and logistic regression were used to diagnose the presence of independent effects of causal coherence, causal status, and relational centrality. Adult classification was driven primarily by coherence when causal links were deterministic (Experiment 1) but showed additional influences of causal status when links were probabilistic (Experiment 2). Children's classification was based primarily on causal coherence in both cases. There was no effect of relational centrality in either age group. These results suggest that the generative model (Rehder, 2003a) provides a good account of causal categorization in children as well as adults.     

Causal learning across domains

Five studies investigated (a) children's ability to use the dependent and independent probabilities of events to make causal inferences and (b) the interaction between such inferences and domain-specific knowledge. In Experiment 1, preschoolers used patterns of dependence and independence to make accurate causal inferences in the domains of biology and psychology. Experiment 2 replicated the results in the domain of biology with a more complex pattern of conditional dependencies. In Experiment 3, children used evidence about patterns of dependence and independence to craft novel interventions across domains. In Experiments 4 and 5, children's sensitivity to patterns of dependence was pitted against their domain-specific knowledge. Children used conditional probabilities to make accurate causal inferences even when asked to violate domain boundaries.