Identifying expectations about the strength of causal relationships

When we try to identify causal relationships, how strong do we expect that relationship to be? Bayesian models of causal induction rely on assumptions regarding people’s a priori beliefs about causal systems, with recent research focusing on people’s expectations about the strength of causes. These expectations are expressed in terms of prior probability distributions. While proposals about the form of such prior distributions have been made previously, many different distributions are possible, making it difficult to test such proposals exhaustively. In Experiment 1 we used iterated learning—a method in which participants make inferences about data generated based on their own responses in previous trials—to estimate participants’ prior beliefs about the strengths of causes. This method produced estimated prior distributions that were quite different from those previously proposed in the literature. Experiment 2 collected a large set of human judgments on the strength of causal relationships to be used as a benchmark for evaluating different models, using stimuli that cover a wider and more systematic set of contingencies than previous research. Using these judgments, we evaluated the predictions of various Bayesian models. The Bayesian model with priors estimated via iterated learning compared favorably against the others. Experiment 3 estimated participants’ prior beliefs concerning different causal systems, revealing key similarities in their expectations across diverse scenarios.     

Causal Information-Seeking Strategies Change Across Childhood and Adolescence

Intervening on causal systems can illuminate their underlying structures. Past work has shown that, relative to adults, young children often make intervention decisions that appear to confirm a single hypothesis rather than those that optimally discriminate alternative hypotheses. Here, we investigated how the ability to make informative causal interventions changes across development. Ninety participants between the ages of 7 and 25 completed 40 different puzzles in which they had to intervene on various causal systems to determine their underlying structures. Each puzzle comprised a three- or four-node computer chip with hidden wires. On each trial, participants viewed two possible arrangements of the chip's hidden wires and had to select a single node to activate. After observing the outcome of their intervention, participants selected a wire configuration and rated their confidence in their selection. We characterized participant choices with a Bayesian measurement model that indexed the extent to which participants selected nodes that would best disambiguate the two possible causal structures versus those that had high causal centrality in one of the two causal hypotheses but did not necessarily discriminate between them. Our model estimates revealed that the use of a discriminatory strategy increased through early adolescence. Further, developmental improvements in intervention strategy were related to changes in the ability to accurately judge the strength of evidence that interventions revealed, as indexed by participants' confidence in their selections. Our results suggest that improvements in causal information-seeking extend into adolescence and may be driven by metacognitive sensitivity to the efficacy of previous interventions in discriminating competing ideas.     

What causal conditional reasoning tells us about people's understanding of causality

Causal conditional reasoning means reasoning from a conditional statement that refers to causal content. We argue that data from causal conditional reasoning tasks tell us something not only about how people interpret conditionals, but also about how they interpret causal relations. In particular, three basic principles of people's causal understanding emerge from previous studies: the modal principle, the exhaustive principle, and the equivalence principle. Restricted to the four classic conditional inferences—Modus Ponens, Modus Tollens, Denial of the Antecedent, and Affirmation of the Consequent—causal conditional reasoning data are only partially able to support these principles. We present three experiments that use concrete and abstract causal scenarios and combine inference tasks with a new type of task in which people reformulate a given causal situation. The results provide evidence for the proposed representational principles. Implications for theories of the naïve understanding of causality are discussed.     

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.     

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.     

The role of learning data in causal reasoning about observations and interventions

Recent studies have shown that people have the capacity to derive interventional predictions for previously unseen actions from observational knowledge, a finding that challenges associative theories of causal learning and reasoning (e.g., Meder, Hagmayer, & Waldmann, 2008). Although some researchers have claimed that such inferences are based mainly on qualitative reasoning about the structure of a causal system (e.g., Sloman, 2005), we propose that people use both the causal structure and its parameters for their inferences. We here employ an observational trial-by-trial learning paradigm to test this prediction. In Experiment 1, the causal strength of the links within a given causal model was varied, whereas in Experiment 2, base rate information was manipulated while keeping the structure of the model constant. The results show that learners’ causal judgments were strongly affected by the observed learning data despite being presented with identical hypotheses about causal structure. The findings show furthermore that participants correctly distinguished between observations and hypothetical interventions. However, they did not adequately differentiate between hypothetical and counterfactual interventions.     

Sticking to the Evidence? A Behavioral and Computational Case Study of Micro‐Theory Change in the Domain of Magnetism

Constructing an intuitive theory from data confronts learners with a “chicken‐and‐egg” problem: The laws can only be expressed in terms of the theory's core concepts, but these concepts are only meaningful in terms of the role they play in the theory's laws; how can a learner discover appropriate concepts and laws simultaneously, knowing neither to begin with? We explore how children can solve this chicken‐and‐egg problem in the domain of magnetism, drawing on perspectives from computational modeling and behavioral experiments. We present 4‐ and 5‐year‐olds with two different simplified magnet‐learning tasks. Children appropriately constrain their beliefs to two hypotheses following ambiguous but informative evidence. Following a critical intervention, they learn the correct theory. In the second study, children infer the correct number of categories given no information about the possible causal laws. Children's hypotheses in these tasks are explained as rational inferences within a Bayesian computational framework.     

Inferring hidden causal structure

We used a new method to assess how people can infer unobserved causal structure from patterns of observed events. Participants were taught to draw causal graphs, and then shown a pattern of associations and interventions on a novel causal system. Given minimal training and no feedback, participants in Experiment 1 used causal graph notation to spontaneously draw structures containing one observed cause, one unobserved common cause, and two unobserved independent causes, depending on the pattern of associations and interventions they saw. We replicated these findings with less-informative training (Experiments 2 and 3) and a new apparatus (Experiment 3) to show that the pattern of data leads to hidden causal inferences across a range of prior constraints on causal knowledge.     

Exemplars, prototypes, similarities, and rules in category representation: an example of hierarchical bayesian analysis

This article demonstrates the potential of using hierarchical Bayesian methods to relate models and data in the cognitive sciences. This is done using a worked example that considers an existing model of category representation, the Varying Abstraction Model (VAM), which attempts to infer the representations people use from their behavior in category learning tasks. The VAM allows for a wide variety of category representations to be inferred, but this article shows how a hierarchical Bayesian analysis can provide a unifying explanation of the representational possibilities using 2 parameters. One parameter controls the emphasis on abstraction in category representations, and the other controls the emphasis on similarity. Using 30 previously published data sets, this work shows how inferences about these parameters, and about the category representations they generate, can be used to evaluate data in terms of the ongoing exemplar versus prototype and similarity versus rules debates in the literature. Using this concrete example, this article emphasizes the advantages of hierarchical Bayesian models in converting model selection problems to parameter estimation problems, and providing one way of specifying theoretically based priors for competing models.     

Constructing a New Theory From Old Ideas and New Evidence

A central tenet of constructivist models of conceptual development is that children's initial conceptual level constrains how they make sense of new evidence and thus whether exposure to evidence will prompt conceptual change. Yet little experimental evidence directly examines this claim for the case of sustained, fundamental conceptual achievements. The present study combined scaling and experimental microgenetic methods to examine the processes underlying conceptual change in the context of an important conceptual achievement of early childhood—the development of a representational theory of mind. Results from 47 children (M age = 3.7 years) indicate that only children who were conceptually close to understanding false belief at the beginning of the study, and who were experimentally exposed to evidence of people acting on false beliefs, reliably developed representational theories of minds. Combined scaling and microgenetic data revealed how prior conceptual level interacts with experience, thereby providing critical experimental evidence for how conceptual change results from the interplay between conceptions and evidence.     

Seeing versus doing: two modes of accessing causal knowledge

The ability to derive predictions for the outcomes of potential actions from observational data is one of the hallmarks of true causal reasoning. We present four learning experiments with deterministic and probabilistic data showing that people indeed make different predictions from causal models, whose parameters were learned in a purely observational learning phase, depending on whether learners believe that an event within the model has been merely observed ("seeing") or was actively manipulated ("doing"). The predictions reflect sensitivity both to the structure of the causal models and to the size of their parameters. This competency is remarkable because the predictions for potential interventions were very different from the patterns that had actually been observed. Whereas associative and probabilistic theories fail, recent developments of causal Bayes net theories provide tools for modeling this competency.     

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.     

Pretense,Counterfactuals, and Bayesian Causal Models: Why What Is Not Real Really Matters

Young children spend a large portion of their time pretending about non‐real situations. Why? We answer this question by using the framework of Bayesian causal models to argue that pretending and counterfactual reasoning engage the same component cognitive abilities: disengaging with current reality, making inferences about an alternative representation of reality, and keeping this representation separate from reality. In turn, according to causal models accounts, counterfactual reasoning is a crucial tool that children need to plan for the future and learn about the world. Both planning with causal models and learning about them require the ability to create false premises and generate conclusions from these premises. We argue that pretending allows children to practice these important cognitive skills. We also consider the prevalence of unrealistic scenarios in children's play and explain how they can be useful in learning, despite appearances to the contrary.     

The advantage of timely intervention

Can people learn causal structure more effectively through intervention rather than observation? Four studies used a trial-based learning paradigm in which participants obtained probabilistic data about a causal chain through either observation or intervention and then selected the causal model most likely to have generated the data. Experiment 1 demonstrated that interveners made more correct model choices than did observers, and Experiments 2 and 3 ruled out explanations for this advantage in terms of informational differences between the 2 conditions. Experiment 4 tested the hypothesis that the advantage was driven by a temporal signal; interveners may exploit the cue that their interventions are the most likely causes of any subsequent changes. Results supported this temporal cue hypothesis.     

Does successfully changing personality traits via intervention require that participants be autonomously motivated to change?

A growing body of research suggests that personality traits can be changed through intervention. Theorists have speculated that successful interventions may require (1) that participants autonomously choose which traits they change and (2) that they be deeply invested in the change process. The present studies tested these propositions by examining whether interventions to change conscientiousness and emotional stability can be successful when (1) participants are randomly assigned traits to change or (2) they are naïve with respect to the intervention’s target trait. Results indicated that participants could be randomly assigned to change conscientiousness—even if they were unaware that the intervention was targeting conscientiousness. In contrast, interventions targeting emotional stability were effective only if participants both (1) autonomously chose to work on emotional stability and (2) received an effective intervention. These findings have practical implications for designing interventions—and they suggest that different traits may develop via different processes.     

The causal psycho-logic of choice

Choices do not merely identify one option among a set of possibilities; choosing is an intervention, an action that changes the world. As a result, good decision making generally requires a model specifying how actions are causally related to outcomes. Interventions license different inferences than observations because an event whose state has been determined by intervention is not diagnostic of the normal causes of that event. We integrate these ideas into a causal framework for decision making based on causal Bayes nets theory, and suggest that deliberate decision making is based on simplified causal models and imaginary interventions. The framework is consistent with what we know so far about how people make decisions.     

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.     

Time as a guide to cause

How do people learn causal structure? In 2 studies, the authors investigated the interplay between temporal-order, intervention, and covariational cues. In Study 1, temporal order overrode covariation information, leading to spurious causal inferences when the temporal cues were misleading. In Study 2, both temporal order and intervention contributed to accurate causal inference well beyond that achievable through covariational data alone. Together, the studies show that people use both temporal-order and interventional cues to infer causal structure and that these cues dominate the available statistical information. A hypothesis-driven account of learning is endorsed, whereby people use cues such as temporal order to generate initial models and then test these models against the incoming covariational data.     

A Bayesian Model of Biases in Artificial Language Learning: The Case of a Word‐Order Universal

In this article, we develop a hierarchical Bayesian model of learning in a general type of artificial language‐learning experiment in which learners are exposed to a mixture of grammars representing the variation present in real learners’ input, particularly at times of language change. The modeling goal is to formalize and quantify hypothesized learning biases. The test case is an experiment ( Culbertson, Smolensky, & Legendre, 2012 ) targeting the learning of word‐order patterns in the nominal domain. The model identifies internal biases of the experimental participants, providing evidence that learners impose (possibly arbitrary) properties on the grammars they learn, potentially resulting in the cross‐linguistic regularities known as typological universals. Learners exposed to mixtures of artificial grammars tended to shift those mixtures in certain ways rather than others; the model reveals how learners’ inferences are systematically affected by specific prior biases. These biases are in line with a typological generalization—Greenberg's Universal 18—which bans a particular word‐order pattern relating nouns, adjectives, and numerals.     

Causal diversity effects in information seeking

When trying to determine the root cause of an observed effect, people may seek out information with which to test a candidate hypothesis. In two studies, we investigated how knowledge of causal structure influences this information-seeking process. Specifically, we asked whether people would choose to test for pieces of evidence that were far apart or close together in the learned causal structure of a disease category. In parallel with findings showing people’s tendency to select diverse evidence in argument testing (López, 1995), our participants tested for evidence distantly located within the causal structure. Simultaneously, they rated the probability of occurrence of such diverse evidence as comparatively low. These findings suggest that rather than seeking out information most likely to confirm the hypothesis, people seek out evidence that they believe will most strongly support the hypothesis if present but that they also believe is relatively unlikely to be present (that is, might disconfirm the hypothesis).