The role of causal models in multiple judgments under uncertainty

Two studies examined a novel prediction of the causal Bayes net approach to judgments under uncertainty, namely that causal knowledge affects the interpretation of statistical evidence obtained over multiple observations. Participants estimated the conditional probability of an uncertain event (breast cancer) given information about the base rate, hit rate (probability of a positive mammogram given cancer) and false positive rate (probability of a positive mammogram in the absence of cancer). Conditional probability estimates were made after observing one or two positive mammograms. Participants exhibited a causal stability effect: there was a smaller increase in estimates of the probability of cancer over multiple positive mammograms when a causal explanation of false positives was provided. This was the case when the judgments were made by different participants (Experiment 1) or by the same participants (Experiment 2). These results show that identical patterns of observed events can lead to different estimates of event probability depending on beliefs about the generative causes of the observations.     

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.     

The role of information presentation formats in belief updating

The effects of the format by which information is presented on the cognitive processes of belief updating were investigated in the present research. Because of the differences in the affordance of verbal vs. numerical information, it is predicted that the belief updating processes involved in processing verbal and numerical information would be different. Specifically, the additive rule is used to combine information using verbal formats, while the averaging rule is used to combine information using numerical formats. Two experiments were conducted to test these hypotheses. Experiment 1 tested the belief updating process in the positive direction, and Experiment 2 tested the process in the negative direction. Two independent variables were manipulated: information presentation format (verbal vs numerical) and presentation order (strong–weak vs weak–strong). The participants were asked to adjust their purchase likelihood of a consumer product based on the sequential presentations of two experts' opinions. These two opinions varied in their formats (verbal vs. numerical) and strengths (strong vs weak). The two opinions were presented in either the strong–weak order or the weak–strong order. Participants were instructed to first anchor their purchase likelihood at 50%, and then adjust the purchase likelihood, first based on the first expert's opinion, and second based on both experts' opinions. In both experiments the hypotheses that participants employed an additive rule to integrate verbal information and an averaging rule to integrate numerical information were supported.     

The role of parametric assumptions in adaptive Bayesian estimation

Variants of adaptive Bayesian procedures for estimating the 5% point on a psychometric function were studied by simulation. Bias and standard error were the criteria to evaluate performance. The results indicated a superiority of (a) uniform priors, (b) model likelihood functions that are odd symmetric about threshold and that have parameter values larger than their counterparts in the psychometric function, (c) stimulus placement at the prior mean, and (d) estimates defined as the posterior mean. Unbiasedness arises in only 10 trials, and 20 trials ensure constant standard errors. The standard error of the estimates equals 0.617 times the inverse of the square root of the number of trials. Other variants yielded bias and larger standard errors.     

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 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.     

Causal powers and preventers: An explanatory account of cue interaction effects in human causal judgement

According to the causal powers theory, all causal relations are understood in terms of causal powers of one thing producing an effect by acting on liability of another thing. Powers can vary in strength, and their operation also depends on the presence of preventers. When an effect occurs, there is a need to account for the occurrence by assigning sufficient strength to produce it to its possible causes. Contingency information is used to estimate strengths of powers and preventers and the extent to which they account for occurrences and nonoccurrences of the outcome. People make causal judgements from contingency information by processes of inference that interpret evidence in terms of this fundamental understanding. From this account it is possible to derive a computational model based on a common set of principles that involve estimating strengths, using these estimates to interpret ambiguous information, and integrating the resultant evidence in a weighted averaging model. It is shown that the model predicts cue interaction effects in human causal judgement, including forward and backward blocking, second and third order backward blocking, forward and backward conditioned inhibition, recovery from overshadowing, superlearning, and backward superlearning.     

Individual differences in information order effects: The importance of right-hemisphere access in belief updating

The order in which information is received alters the evaluation of causal hypotheses. Specifically, research suggests that the last piece of information oftentimes has the greatest impact on the evaluation and that the difference in subjective value between two pieces of information is an important factor influencing the magnitude of this recency effect. The present paper extends this line of work by exploring individual differences in this phenomenon via one's degree of handedness. Two hundred and five participants were given two hypothetical scenarios and related causal hypotheses accompanied by two pieces of additional information and asked to revise their belief in each hypothesis as information accumulated. Results confirmed predictions that 1) inconsistent/mixed-handers (those who use their non-dominant hand for at least some activities) show a larger effect with two pieces of inconsistent weak or strong information, and 2) neither mixed-handers nor consistent/strong-handers (those who use their dominant hand for almost all activities) show an effect with strong and weak pieces of consistent information. Mixed-handers' susceptibility to persuasive arguments and Ramachandran’s (1995; Ramachandran and Blakeslee, 1998) belief-updating theory centered around communication between the two halves of the brain and functional access to the right hemisphere are used to account for these data.     

Attention and expectation in human predictive learning: The role of uncertainty

Three localized, visual pattern stimuli were trained as predictive signals of auditory outcomes. One signal partially predicted an aversive noise in Experiment 1 and a neutral tone in Experiment 2, whereas the other signals consistently predicted either the occurrence or absence of the noise. The expectation of the noise was measured during each signal presentation, and only participants for whom this expectation demonstrated contingency knowledge showed differential attention to the signals. Importantly, when attention was measured by visual fixations, the contingency-aware group attended more to the partially predictive signal than to the consistent predictors in both experiments. This profile of visual attention supports the Pearce and Hall (1980) Pearce, J. M. and Hall, G. 1980. A model for Pavlovian learning: Variations in the effectiveness of conditioned but not unconditioned stimuli. Psychological Review, 87: 532–552. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar] theory of the role of attention in associative learning.     

The role of cultural orientation in bargaining under incomplete information: Differences in causal attributions

This research examines how differences in cultural orientation influence causal attributions and thus the behavioral outcomes in an incomplete information bargaining situation. Using ultimatum bargaining, three experiments demonstrate that acceptance rates differ across Western and East Asian cultures because of the differences in implicit theories of behavior. The results of Experiment 1 shows that East Asians are more sensitive to both external constraints and group influences but only when there is information about the opponent’s situation to discount personality traits. Experiment 2 shows that reasons for an opponent’s behavior mediate the influence of cultural orientation on bargaining outcomes when situational constraints are made salient. Experiment 3 shows that reasons for an opponent’s behavior based on the saliency of a group context mediate the influence of cultural orientation on behavior. The paper concludes by discussing the implications of the findings and suggesting directions for future research.     

Episodic memory updating: The role of context familiarity

We previously demonstrated that spatial context is a powerful reminder that can trigger memory updating (Hupbach, Hardt, Gomez, & Nadel in Learning & Memory, 15, 574–579 2008). In the present study, we asked whether the familiarity of the spatial context modulates the role of spatial context as a reminder. Since context familiarity can be easily manipulated in children, we chose 5-year-olds as study participants. In two experiments, we demonstrated robust memory-updating effects in children. Spatial context triggered incorporation of new information into old memories only when the context was unfamiliar. In highly familiar spatial environments (children’s homes), spatial context did not initiate memory updating. Other reminders (the experimenter and a reminder question) became highly effective in familiar contexts. These findings shed further light on the specific conditions that trigger memory updating and support the view that the mechanisms underlying it are similar in children and adults.     

Perceiving a strong causal relation in a weak contingency: Further investigation of the evidential evaluation model of causal judgement

Contingency information is information about the occurrence or nonoccurrence of a certain effect in the presence or absence of a candidate cause. An objective measure of contingency is the δP rule, which involves subtracting the probability of occurrence of an effect when a causal candidate is absent from the probability of occurrence of the effect when the candidate is present. Causal judgements conform closely to δP but deviate from it under certain circumstances. Three experiments show that such deviations can be predicted by a model of causal judgement that has two components: a rule of evidence, that causal judgement is a function of the proportion of relevant instances that are judged to be confirmatory for the causal candidate, and a tendency for information about instances in which the candidate is present to have greater effect on judgement than instances in which the candidate is absent. Two experiments demonstrate how this model accounts for some recently published findings. A third experiment shows that it is possible to use the model to predict the occurrence of high causal judgements when the objective contingency is close to zero.     

Attention and expectation in human predictive learning: the role of uncertainty

Three localized, visual pattern stimuli were trained as predictive signals of auditory outcomes. One signal partially predicted an aversive noise in Experiment 1 and a neutral tone in Experiment 2, whereas the other signals consistently predicted either the occurrence or absence of the noise. The expectation of the noise was measured during each signal presentation, and only participants for whom this expectation demonstrated contingency knowledge showed differential attention to the signals. Importantly, when attention was measured by visual fixations, the contingency-aware group attended more to the partially predictive signal than to the consistent predictors in both experiments. This profile of visual attention supports the Pearce and Hall (1980) theory of the role of attention in associative learning.     

The role of causal attributions in competitive situations

Previous data have shown that successful women are judged to have masculine characteristics [J. A. Doyle (1989), The Male Experience(2nd ed.), Dubuque, IA: Wm. C. Brown; D. L. Gill (1986), Psychological Dynamics of Sport,Champaign, IL: Human Kinetics; D. J. Murphy (1988), “Sport and Gender,” in W. M. Leonard II (Ed.), A Sociological Perspective of Sport(3rd ed.), New York: Macmillan; P. Willis (1994), “Women in Sport in Ideology,” in S. Birrell and C. L. Cole (Eds.), Women, Sport, and Culture,Champaign, IL: Human Kinetics]. Two experiments were conducted to test two different explanations for this effect, the appraisal and attribution hypotheses. In Experiment 1, male participants who lost to a female confederate on a masculine-relevant task rated her as having more masculine and fewer feminine characteristics than when the task was described as feminine-relevant. However, heart rate and blood pressure data failed to support the appraisal hypothesis that these reactions were due to the stress of losing to the female, or defensiveness. The alternative hypothesis that these ratings were due to standard attributional processes was more consistent with the data. Consequently, this hypothesis was tested in Experiment 2 using an attributional paradigm. Consistent with Experiment 1, the attribution hypothesis fared better than did the appraisal hypothesis.     

Cue interaction effects in causal judgement: An interpretation in terms of the evidential evaluation model

In judging the extent to which a cue causes an outcome, judgement can be affected by information about other cues that are correlated with the one being judged. These cue interaction effects have usually been interpreted in terms of associative learning processes. I propose that a different model of causal judgement, the evidential evaluation model, offers a viable alternative interpretation of cue interaction phenomena. Under the evidential evaluation model, instances of contingency information are interpreted as evidence, which is confirmatory, disconfirmatory, or irrelevant for the cue being judged. When two cues co-occur in a set of instances the evidential value of the instances for one of them is determined by three factors: the proportion of confirming instances in the set; disambiguation value, which concerns the relation between the set of information and prior beliefs about the co-occurring cue; and confirmation value, which concerns the relation between the set of information and prior beliefs about the cue being judged. Any previous judgement of the cue is then modified in the light of these. It is shown that this model can account for all the cue interaction phenomena that have been investigated in studies of human causal judgement. The model also generates novel predictions, and the results of three experiments give support to these predictions. It is also shown that several other current models of causal judgement fail to predict a key result from Experiment 3.     

The causal role of interpretive bias in anxiety reactivity

Elevated anxiety vulnerability is associated with a tendency to interpret ambiguous stimuli as threatening, but the causal basis of this relationship has not been established. Recently, procedures have been developed to systematically manipulate interpretive bias, but the impact of such manipulation on anxiety reactivity to a subsequent stressor has not yet been examined. In the present study, training procedures were used to induce interpretive biases favoring the threatening or nonthreatening meanings of ambiguous information in a sample of 48 undergraduate students. Following this interpretive training, participants' emotional reactions to a stressful video were assessed. The finding that the manipulation of interpretive bias modified emotional reactivity supports the hypothesis that interpretive bias can indeed play a causal role in anxiety vulnerability.     

The role of contrast in causal and explanatory claims

Following Dretske (1977), there has been a considerable body of literature on the role of contrastive stress in causal claims. Following van Fraassen (1980), there has been a considerable body of literature on the role of contrastive stress in explanations and explanation-requesting why-questions. Amazingly, the two bodies of literature have remained almost entirely disjoint. With an understanding of the contrastive nature of ordinary causal claims, and of the linguistic roles of contrastive stress, it is possible to provide a unified account of both phenomena. I provide such an account from within the framework of a probabilistic theory of causation. Relations of screening-off, long familiar to researchers in probabilistic causality, play a central role in this account.I would like to thank the following people for comments upon earlier drafts of this paper: Frank Arntzenius, Eric Barnes, Nuel Belnap, Alex Byrne, John Carroll, Fiona Cowie, Alan Hájek, David Hilbert, Carl Hoefer, Marc Lange, Wes Salmon, Cindy Stern, Nigel Thomas, and Jim Woodward.     

The role of causal discourse structure in narrative writing

All writers produce text content and ideally connect it together according to discourse conventions. We investigate whether a particularly strong discourse convention, the need for causal coherence in narratives, can predict the kind of text writers will produce. Causality has been found to be a significant discourse factor in reading comprehension and hence can be expected to determine also what writers produce during composition. In Experiment 1, writers composed short continuations at various points throughout a simple narrative, whereas in Experiment 2, writers composed continuations to complete several narratives. The results indicate that causality indeed plays a major role in composition. Writers tend to produce new text in such a way that it is causally connected to the prior text. Furthermore, writers favored causal relations of necessity or of necessity and sufficiency while largely avoiding relations of sufficiency alone, which suggests a general discourse constraint to be maximally informative (e.g., Grice, 1975).