Causal judgement as evaluation of evidence: The use of confirmatory and disconfirrnatory information

There are four kinds of contingency information: occurrences and nonoccurrences of an effect in the presence and absence of a cause. In two experiments participants made judgements about sets of stimulus materials in which one of these four kinds had zero frequency. The experiments tested two kinds of predictions derived from the evidential evaluation model of causal judgement, which postulates that causal judgement depends on the proportion of instances evaluated as confirmatory for the cause being judged. The model predicts significant effects of manipulating the frequency of one kind of contingency information in the absence of changes in the objective contingency. The model also predicts that extra weight will be given to one kind of confirmatory information when the other kind has zero frequency, and to one kind of disconfirmatory information when the other kind has zero frequency. Results supported both sets of predictions, and also disconfirmed predictions of the power probabilistic contrast theory of causal judgement. This research therefore favours an account of causal judgement in which contingency information is transformed into evidence, and judgement is based on the net confirmatory or disconfirmatory value of the evidence.     

Causal attribution from covariation information: the evidential evaluation model

It is hypothesized that causal attributions are made by transforming covariation information into evidence according to notions of evidential value, and that causal judgement is a function of the proportion of instances that are evaluated as confirmatory for the causal hypothesis under test: this is called the evidential evaluation model. An experiment was designed to test the judgemental rule in this model by setting up problems presenting consensus, distinctiveness, and consistency information in which the proportion of confirmatory instances varied but the objective contingency did not. It was found that judgements tended to vary with the proportion of confirmatory instances. Several other current models of causal judgement or causal attribution fail to account for this result. Similar findings have been obtained in studies of causal judgement from contingency information, so the present findings support an argument that the evidential evaluation model provides a unified account of judgement in both domains. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

The impact of domain-specific beliefs on decisions and causal judgments

Extensive evidence suggests that people often rely on their causal beliefs in their decisions and causal judgments. To date, however, there is a dearth of research comparing the impact of causal beliefs in different domains. We conducted two experiments to map the influence of domain-specific causal beliefs on the evaluation of empirical evidence when making decisions and subsequent causal judgments. Participants made 120 decisions in a two-alternative forced-choice task, framed in either a medical or a financial domain. Before each decision, participants could actively search for information about the outcome (“occurrence of a disease” or “decrease in a company's share price”) on the basis of four cues. To analyze the strength of causal beliefs, we set two cues to have a generative relation to the outcome and two to have a preventive relation to the outcome. To examine the influence of empirical evidence, we manipulated the predictive power (i.e., cue validities) of the cues. Both experiments included a validity switch, where the four selectable cues switched from high to low validity or vice versa. Participants had to make a causal judgment about each cue before and after the validity switch. In the medical domain, participants stuck to the causal information in causal judgments, even when evidence was contradictory, while decisions showed an effect of both empirical and causal information. In contrast, in the financial domain, participants mainly adapted their decisions and judgments to the cue validities. We conclude that the strength of causal beliefs (1) is shaped by the domain, and (2) has a differential influence on the degree to which empirical evidence is taken into account in causal judgments and decision making.     

Interaction between previous beliefs and cue predictive value in covariation-based causal induction

The main aim of this work was to show the impact of preexisting causal beliefs on causal induction from cause-effect co-occurrence information, when several cues compete with each other for predicting the same effect. Two different causal scenarios -- one social (a), the other medical (b) -- were used to check the generality of the effects. In Experiments 1a and 1b, participants were provided information on the co-occurrence of a two-cause compound and an effect, but not about the potential relationship between each cause by its own and the effect. As expected, prior beliefs -- induced by means of instructions -- strongly modulated the causal strength assigned to each element of the compound. In Experiments 2a and 2b, covariation evidence was provided, not only about the predictive value of the two-cause compound, but also about one of the elements of the compound. When this evidence was available, prior beliefs had less impact on judgments, and these were mostly guided by the relative predictive value of the cue. These results demonstrate the involvement of inferential integrative mechanisms in the generation of causal knowledge and show that single covariation detection mechanisms -- either rule-based or associative -- are insufficient to account for human causal judgment. At the same time, the fact that the power of new covariational evidence to change prior beliefs depended on the availability of information on the relative (conditional) predictive value of the target candidate cause suggests that causal knowledge derived from information on causal mechanisms and from covariation probably share a common representational basis.     

Reconciling Compensatory and Noncompensatory Strategies of Cue Weighting: A Causal Model Approach

When forming a judgment about any unknown item, people must draw inferences from information that is already known. This paper examines causal relationships between cues as a relevant factor influencing how people determine the amount of weight to place on each piece of available evidence. We propose that people draw from their beliefs about specific causal relationships between cues when determining how much weight to place on those cues, and that understanding this process can help reconcile differences between predictions of compensatory and lexicographic heuristic strategies. As causal relationships change, different cues become more or less important. Across three experiments, we find support for the use of causal models in determining cue weights, but leave open the possibility that they work in concert with other strategies as well. We conclude by discussing relative strengths and weaknesses of the causal model approach relative to existing models, and suggest areas for future research. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Trial order affects cue interaction in contingency judgment.

Recent research on contingency judgment indicates that the judged predictiveness of a cue is dependent on the predictive strengths of other cues. Two classes of models correctly predict such cue interaction: associative models and statistical models. However, these models differ in their predictions about the effect of trial order on cue interaction. In five experiments reported here, college students viewed trial-by-trial data regarding several medical symptoms and a disease, judging the predictive strength of each symptom with respect to the disease. The results indicate that trial order influences the manner in which cues interact, but that neither the associative nor the statistical models can fully account for the data pattern. A possible variation of an associative account is discussed.     

Cue interaction and judgments of causality: Contributions of causal and associative processes

In four experiments, the predictions made by causal model theory and the Rescorla-Wagner model were tested by using a cue interaction paradigm that measures the relative response to a given event based on the influence or salience of an alternative event. Experiments 1 and 2 uncorrelated two variables that have typically been confounded in the literature (causal order and the number of cues and outcomes) and demonstrated that overall contingency judgments are influenced by the causal structure of the events. Experiment 3 showed that trial-by-trial prediction responses, a second measure of causal assessment, were not influenced by the causal structure of the described events. Experiment 4 revealed that participants became less sensitive to the influence of the causal structure in both their ratings and their predictions as trials progressed. Thus, two experiments provided evidence for high-level (causal reasoning) processes, and two experiments provided evidence for low-level (associative) processes. We argue that both factors influence causal assessment, depending on what is being asked about the events and participants' experience with those events.     

Causal judgement from contingency information: Judging interactions between two causal candidates

In two experiments participants judged the extent to which occurrences and non-occurrences of an effect could be attributed to an interaction between two causal candidates A and B. In Experiment 1 judgements were influenced by the proportion of instances normatively evaluated as confirmatory for the interaction interpretation, when the objective contingency was held constant. Information about instances in which both candidates were present and the effect occurred was more influential than information about instances in which both candidates were absent and the effect did not occur. In Experiment 2 the occurrence rate of the effect when both candidates were present, when A alone was present, when B alone was present, and when both were absent was manipulated. Interaction judgements were mainly determined by occurrence rate when both were present. There was also a significant effect of occurrence rate when both were absent, but the other two occurrence rates had no significant effect. These results are interpreted as supporting a general model in which causal judgements are made according to the proportion of instances evaluated as supporting the interpretation being judged.     

Higher-order retrospective revaluation in human causal learning

Previous studies demonstrated that participants will retrospectively adjust their ratings about the relation between a target cue and an outcome on the basis of information about the causal status of a competing cue that was previously paired with the target cue. We demonstrate that such retrospective revaluation effects occur not only for target cues with which the competing cue was associated directly, but also for target cues that were associated indirectly with the competing cue. These second-order and third-order retrospective revaluation effects are compatible with certain implementations of the probabilistic contrast model and with a modified, extended comparator model, but cannot be explained on the basis of a revised Rescorla-Wagner model or a revised SOP model.     

Accounting for occurrences: An explanation for some novel tendencies in causal judgment from contingency information

Contingency information is information about empirical associations between possible causes and outcomes. In the present research, it is shown that, under some circumstances, there is a tendency for negative contingencies to lead to positive causal judgments and for positive contingencies to lead to negative causal judgments. If there is a high proportion of instances in which a candidate cause (CC) being judged is present, these tendencies are predicted by weighted averaging models of causal judgment. If the proportion of such instances is low, the predictions of weighted averaging models break down. It is argued that one of the main aims of causal judgment is to account for occurrences of the outcome. Thus, a CC is not given a high causal judgment if there are few or no occurrences of it, regardless of the objective contingency. This argument predicts that, if there is a low proportion of instances in which a CC is present, causal judgments are determined mainly by the number of Cell A instances (i.e., CC present, outcome occurs), and that this explains why weighted averaging models fail to predict judgmental tendencies under these circumstances. Experimental results support this argument.     

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.     

Missing information in multiple-cue probability learning

In a multiple-cue probability learning task, participants learned to use six discrete symptoms (i.e., cues) to diagnose which of three possible flu strains a hypothetical patient suffered from. For some patients, information regarding the status of certain symptoms was not available. Various possible ways in which the missing cue information might be processed were distinguished and tested in a series of three experiments (Ns = 80, 109, and 61). The results suggest that the judged probability of the outcome variable (i.e., flu strain) was assessed by "filling in" the missing cue information with a mean value based on previous observations. The predictions of other methods of processing missing cue information are inconsistent with the data.     

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.     

Predictions and causal estimations are not supported by the same associative structure

Studies performed by different researchers have shown that judgements about cue-outcome relationships are systematically influenced by the type of question used to request those judgements. It is now recognized that judgements about the strength of the causal link between a cue and an outcome are mostly determined by the cue-outcome contingency, whereas predictions of the outcome are more influenced by the probability of the outcome given the cue. Although these results make clear that those different types of judgement are mediated by some knowledge of the normative differences between causal estimations and outcome predictions, they do not speak to the underlying processes of these effects. The experiment presented here reveals an interaction between the type of question and the order of trials that challenges standard models of causal and predictive learning that are framed exclusively in associative terms or exclusively in higher order reasoning terms. However, this evidence could be easily explained by assuming the combined intervention of both types of process.     

Judgement of two causal candidates from contingency information: II. Effects of information about one cause on judgements of the other cause

When judgements are being made about two causes there are eight possible kinds of contingency information: occurrences and nonoccurrences of the outcome when both causes are present, when Cause 1 alone is present, when Cause 2 alone is present, and when neither cause is present. It is proposed that contingency information is used to some extent to judge proportionate strength, which is the proportion of occurrences of the outcome that each cause can account for. This leads to a prediction that judgements of one cause will be influenced by information about occurrences, but not nonoccurrences, of the outcome when only the other cause is present. In six experiments consistent support was found for this prediction when the cause being judged had a positive relation with the outcome, but no consistent tendency was found when the cause being judged had a negative relation with the outcome. The effects found for causes with positive contingency cannot be explained by the Rescorla-Wagner model of causal judgement nor by the hypothesis that causal judgements are based on conditional contingencies.     

经验信息与共变信息对判断两原因共同作用的影响

本研究考察了被试在使用经验信息和共变信息进行两原因共同作用因果判断时所具有的特点。研究结果表明:(1)两原因的性质对于被试的选择有着显著影响。当两原因的可信度相等时,更多被试认为两原因都可以引起结果。(2)两原因都不出现时结果出现的概率P(e/~i~j)对于被试的选择没有显著影响。(3)两原因单独出现时结果出现的概率对于被试的选择有着显著的影响,但是这一变量是与两原因的可信程度共同产生影响的。