Cognitive shortcuts in causal inference

Abstract

The paper explores the idea that causality-based probability judgments are determined by two competing drives: one towards veridicality and one towards effort reduction. Participants were taught the causal structure of novel categories and asked to make predictive and diagnostic probability judgments about the features of category exemplars. We found that participants violated the predictions of a normative causal Bayesian network model because they ignored relevant variables (Experiments 1–3) and because they failed to integrate over hidden variables (Experiment 2). When the task was made easier by stating whether alternative causes were present or absent as opposed to uncertain, judgments approximated the normative predictions (Experiment 3). We conclude that augmenting the popular causal Bayes net computational framework with cognitive shortcuts that reduce processing demands can provide a more complete account of causal inference.

Keywords:

• cognitive science<interdisciplinary links with computational argument
• conditionals<interdisciplinary links with computational argument
• mental models<interdisciplinary links with computational argument
• rationality<interdisciplinary links with computational argument
• computational accounts of probabilistic argument
• explanation

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Erratum

Notes

Probabilities shown in Figure 2 were generated assuming the base rate of the cause features (P _c) within category members was 0.67. Thus, because subjects were not given any information about feature base rates, the predictions are ordinal only (they only reflect the relative strength of each kind of inference).

The probability of the cause given the absence of the effect is given by

This effect is nonnormative if one interprets the causal links as having a single sense, that is, if (in Myastars for example) high density causes a large number of planets but not that low density causes a small number of planets. Under this interpretation, focal cause strength should not affect inferences (e.g. the strength of the causal link between high density and a large number of planets is irrelevant for those Myastars with low density). However, this effect can be understood if a minority of subjects interpreted the causal links as having a dual sense, that is, if “high density causes a large number of planets” also meant that “low density causes a small number of planets”. In this case, the focal cause strength becomes relevant to inferences (E is less likely as strength increases because not-C is more likely to produce not-E). We will address this possible dual sense interpretation of the causal links with a minor change in the wording of the materials in Experiment 2.

This effect is not predicted by the normative model (under either the dual or single sense interpretations of the causal links) or by the effort reduction framework. It did not replicate in the following experiment and so it will not be discussed further.

As in Experiment 1, these (ordinal) predictions were generated assuming that P _c=0.67. In addition, predictions in the explicit condition were generated assuming a base rate of 0.67 for each alternative cause and that each E _i had no causes other than C _i and A _i.

Figure 7(C) shows that inferences were appropriately sensitive to the strength of alternative causes in both the implicit and explicit conditions, although this effect was larger in the implicit condition (9.9 vs. 5.6) than the explicit one (7.4 vs. 6.3), consistent with the normative model (Figure 6(C)). A 2×2 ANOVA revealed an effect of alternative strength, F(1, 94)=44.61, , p<0.0001, a marginal effect of alternative cause type, F(1, 94)=3.37, , p=0.07, and a interaction, F(1, 94)=15.89, , p<0.0001, reflecting the larger effect of alternative cause strength in the implicit condition. Finally, Figure 7(D) shows that inferences were correctly insensitive to alternative cause strength; an ANOVA revealed no main effects and no interaction, all p’s >0.20.

We thank Michael Waldmann for suggesting this manipulation.