Two causal theories of counterfactual conditionals

Bayes nets are formal representations of causal systems that many psychologists have claimed as plausible mental representations. One purported advantage of Bayes nets is that they may provide a theory of counterfactual conditionals, such as If Calvin had been at the party, Miriam would have left early. This article compares two proposed Bayes net theories as models of people's understanding of counterfactuals. Experiments 1-3 show that neither theory makes correct predictions about backtracking counterfactuals (in which the event of the if-clause occurs after the event of the then-clause), and Experiment 4 shows the same is true of forward counterfactuals. An amended version of one of the approaches, however, can provide a more accurate account of these data.     

The mental representation of causal conditional reasoning: mental models or causal models

In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals—such as if P₁then Q and if P₂then Q—are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P_icauses of Q; or symptoms caused byQ. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a “collider” structure where the two causes (P_i) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P_i) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.     

The role of mechanism and covariation information in causal belief updating

The present study is aimed at identifying how prior causal beliefs and covariation information contribute to belief updating when evidence, either compatible or contradictory with those beliefs, is provided. Participants were presented with a cover story with which it was intended to activate or generate a causal belief. Variables related to the prior belief (the type of information, the strength of the cause-effect causal link, and how confident the participant was that the link existed) were assessed. Subsequently, participants were presented with covariational information and were asked to update their beliefs in light of the new evidence. Information reliability, prior belief's causal influence magnitude, and the cause-effect level of contingency portrayed by the new information--but not the type of the prior belief--are shown to directly determine belief updating.     

Probability matching in choice under uncertainty: Intuition versus deliberation

Gaissmaier and Schooler (2008) [Gaissmaier, W., & Schooler, L. J. (2008). The smart potential behind probability matching. Cognition, 109, 416-422] argue that probability matching, which has traditionally been viewed as a decision making error, may instead reflect an adaptive response to environments in which outcomes potentially follow predictable patterns. In choices involving monetary stakes, we find that probability matching persists even when it is not possible to identify or exploit outcome patterns and that many “probability matchers” rate an alternative strategy (maximizing) as superior when it is described to them. Probability matching appears to reflect a mistaken intuition that can be, but often is not, overridden by deliberate consideration of alternative choice strategies.     

The power of causal beliefs and conflicting evidence on causal judgments and decision making

In two experiments, we investigated the relative impact of causal beliefs and empirical evidence on both decision making and causal judgments, and whether this relative impact could be altered by previous experience. Participants had to decide which of two alternatives would attain a higher outcome on the basis of four cues. After completing the decision task, they were asked to estimate to what extent each cue was a reliable cause of the outcome. Participants were provided with instructions that causally related two of the cues to the outcome, whereas they received neutral information about the other two cues. Two of the four cues—a causal and a neutral cue—had high validity and were both generative. The remaining two cues had low validity, and were generative in Experiment 1, but almost not related to the outcome in Experiment 2. Selected groups of participants in both experiments received pre-training with either causal or neutral cues, or no pre-training was provided. Results revealed that the impact of causal beliefs and empirical evidence depends on both the experienced pre-training and cue validity. When all cues were generative and participants received pre-training with causal cues, they mostly relied on their causal beliefs, whereas they relied on empirical evidence when they received pre-training with neutral cues. In contrast, when some of the cues were almost not related to the outcome, participants’ responses were primarily influenced by validity and—to a lesser extent—by causal beliefs. In either case, however, the influence of causal beliefs was higher in causal judgments than in decision making. While current theoretical approaches in causal learning focus either on the effect of causal beliefs or empirical evidence, the present research shows that both factors are required to explain the flexibility involved in human inferences.     

Adjusting for the correspondence bias: Effects of causal uncertainty, cognitive busyness, and causal strength of situational information

This research examined the conditions under which people who have more chronic doubt about their ability to make sense of social behavior (i.e., are causally uncertain; [Weary and Edwards, 1994] and [Weary and Edwards, 1996]) are more likely to adjust their dispositional inferences for a target’s behaviors. Using a cognitive busyness manipulation within the attitude attribution paradigm, we found in Study 1 that higher causal uncertainty predicted increased correction of dispositional inferences, but only when participants had sufficient attentional resources to devote to the task. In Study 2, we found that higher-causal uncertainty predicted greater inferential correction, but only when the additional information provided a more compelling alternative explanation for the observed behavior. Results of this research are discussed in terms of their relevance to the Causal Uncertainty (Weary & Edwards, 1994) and dispositional inference models.     

Immediate and delayed effects of causal uncertainty inductions on uncertainty accessibility

Previous research has focused on enhanced processing as a response to causal uncertainty (CU), but relatively little empirical attention has been given to how CU is activated and the temporal unfolding of this activation. The current research investigates the counterintuitive idea that people inhibit causal uncertainty immediately after its activation. We find that this inhibition weakens over time. Study 1 demonstrates this inhibition effect with self-report uncertainty. Study 2 demonstrates this effect with an implicit accessibility measure. Temporary inhibition of uncertainty may be a general response when uncertainty is activated.     

The effects of statistical training on choice heuristics in choice under uncertainty

Kahneman and Tversky (1984) proposed that decision makers perceive choice uncertainty in two ways: (1) as a distribution of possible outcomes or (2) as a single uncertain outcome. Using statistical training as a factor that influences these perceptions, and thus the type of decision approach individuals use, we found that individuals with different levels of experience displayed differences in the decisions they made and in the choice heuristics used to make those decisions. Statistically naive individuals were more likely to prefer loss-minimizing alternatives, use a more non-compensatory heuristic, and spend more time on loss-related information than their statistically experienced counterparts. When a distributional cue, indicating the distributional nature of choice outcomes, was presented to both experience groups, the naive group was found to use a decision approach similar to the experienced group and to make similar decisions. The results are discussed in terms of the need to include factors that alter individuals' approaches to uncertainty in future behavioral models of uncertain choice.     

Bayesian networks as models of human judgement under uncertainty: The role of causal assumptions in belief updating

Zusammenfassung. Bei der Modellierung der Revision von Überzeugungsstärken wurde in der Vergangenheit die Bedeutung bestehender Annahmen über eine Wissensdomäne für die Evaluation neuer Information vernachlässigt. Im Gegensatz dazu wird in der vorliegenden Arbeit ein Ansatz auf der Basis Bayesscher Netze vorgeschlagen, der eine Einbeziehung subjektiver Annahmen über kausale Zusammenhänge von Ereignissen in einer Domäne erlaubt. Ziel dieser Untersuchung ist es zu überprüfen, ob Urteiler die kausale Rolle einer neuen Evidenz in ihr Revisionsurteil einbeziehen und inwieweit Bayessche Netze geeignet sind, die relevanten Determinanten der Einbeziehung zu beschreiben. Es werden Daten aus zwei Experimenten und Vergleiche mit den Vorhersagen eines Bayesschen Netzes vorgestellt. Die Ergebnisse zeigen, daß das verwendete Bayessche Netz die Urteile von Probanden nicht nur gut, sondern auch besser als zwei alternative Modelle vorhersagt. Mögliche Konsequenzen für die Bewertung der Rationalität menschlicher Urteilsprozesse werden diskutiert. Summary. In modeling processes that underlie the updating of degrees of belief, researchers have often neglected the role of subjects' assumptions concerning causal relationships between new information and contextual variables in a specific domain of reasoning. In contrast, this paper presents a modeling approach which, based on the theory of Bayesian networks, takes into account subjects' beliefs about specific causes and effects in the domain and specifies in which way these beliefs constrain the evaluation of new information. Data from two experiments are described. The experiments were designed to test whether subjects take into account causal relationships as described by a Bayesian network. The results show that the Bayesian network predicts subjects' updates quite precisely and more accurately than two other models. Implications for the appraisal of human rationality in judgement and decision making are discussed.     

Learning the form of causal relationships using hierarchical bayesian models

People learn quickly when reasoning about causal relationships, making inferences from limited data and avoiding spurious inferences. Efficient learning depends on abstract knowledge, which is often domain or context specific, and much of it must be learned. While such knowledge effects are well documented, little is known about exactly how we acquire knowledge that constrains learning. This work focuses on knowledge of the functional form of causal relationships; there are many kinds of relationships that can apply between causes and their effects, and knowledge of the form such a relationship takes is important in order to quickly identify the real causes of an observed effect. We developed a hierarchical Bayesian model of the acquisition of knowledge of the functional form of causal relationships and tested it in five experimental studies, considering disjunctive and conjunctive relationships, failure rates, and cross-domain effects. The Bayesian model accurately predicted human judgments and outperformed several alternative models.     

The role of causal models in analogical inference

Computational models of analogy have assumed that the strength of an inductive inference about the target is based directly on similarity of the analogs and in particular on shared higher order relations. In contrast, work in philosophy of science suggests that analogical inference is also guided by causal models of the source and target. In 3 experiments, the authors explored the possibility that people may use causal models to assess the strength of analogical inferences. Experiments 1-2 showed that reducing analogical overlap by eliminating a shared causal relation (a preventive cause present in the source) from the target increased inductive strength even though it decreased similarity of the analogs. These findings were extended in Experiment 3 to cross-domain analogical inferences based on correspondences between higher order causal relations. Analogical inference appears to be mediated by building and then running a causal model. The implications of the present findings for theories of both analogy and causal inference are discussed.     

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.     

The illusion of knowledge: When more information reduces accuracy and increases confidence

Intuition suggests that having more information can increase prediction accuracy of uncertain outcomes. In four experiments, we show that more knowledge can decrease accuracy and simultaneously increase prediction confidence. Participants were asked to predict basketball games sampled from a National Basketball Association season. All participants were provided with statistics (win record, halftime score), while half were additionally given the team names. Knowledge of names increased the confidence of basketball fans consistent with their belief that this knowledge improved their predictions. Contrary to this belief, it decreased the participants’ accuracy by reducing their reliance on statistical cues. One of the factors contributing to this underweighting of statistical cues was a bias to bet on more familiar teams against the statistical odds. Finally, in a real betting experiment, fans earned less money if they knew the team names while persisting in their belief that this knowledge improved their predictions.     

Remarks on the identifiability of thurstonian paired comparison models under multiple judgment

It is well-known that the representations of the Thurstonian models for difference judgment data are not unique. It has been shown that equivalence classes can be formed to provide a more meaningful partition of the covariance structures of the Thurstonian ranking models. In this paper, we examine the equivalence relations between Thurstonian covariance structure models for paired comparison data obtained under multiple judgment and discuss their implications on the general identification constraints and methods to check for parameter identifiability in restricted models.The author is indebted to Ulf Böckenholt and Albert Maydeu-Olivares for their significant comments and suggestions which led to considerable improvement in this article.     

Unpacking the role of self-esteem in career uncertainty: A self-determination perspective

The aim of this study is to explain why students with high self-esteem have lower career uncertainty than students with low self-esteem. Based on self-determination theory, students with high self-esteem would have higher efficacy in making decisions, which would encourage them to choose a major for self-concordance, such as interest and ability, and increase their course involvement. Both factors are assumed to be related to lower career uncertainty. Data from a national survey of the Taiwan Higher Education Database within the Survey Research Data Archive from juniors at 92 colleges and universities in Taiwan (N = 7418) were analyzed to examine the model. Results supported the proposed model by showing that students with high self-esteem had lower career uncertainty because they chose a major for self-concordant reasons and had a strong motivation to learn, both of which contribute to lower career uncertainty.     

Perception of causal relations in humans: Factors affecting judgments of response-outcome contingencies under free-operant procedures

In three experiments, college studients responded to and rated a range of positive, random, and negative response-outcome contingencies presented in free-operant formats. These experiments sought a paradigm that would yield sensitive and unbiased judgments of response-outcome relations and explored the role of time in the judgment of response-outcome covariation. In Experiment 1, the effects of making continuous and discrete responses on subjects' contingency judgments were compared. In Experiment 2, the effects of changing the temporal definition of discrete responses were examined as were the effects of the amount of exposure to contingency problems. In Experiment 3, the effects of temporal regularity in defining response occurrence and nonoccurrence were investigated. In all three experiments, subjects' judgments were strong linear functions of the programmed contingencies between telegraph key operation and the illumination of a brief light. This result shows free-operant scheduling of response-outcome contingencies to be a highly sensitive and unbiased method of investigating causal perception. Additionally, judgment accuracy was found to be higher for males than for females and to improve as the probability of the subject's making a recorded response rose from .00 toward .50. Finally, a correlational analysis of several possible judgment rules supported the conclusion that subjects rated response-outcome relations on the basis of the difference in the probability of an outcome given their having recently made or not made a response.