Causal judgements about two causal candidates: Accounting for occurrences, estimating strength, and the importance of interaction judgements

Abstract

When two possible causes of an outcome are under consideration, contingency information concerns each possible combination of presence and absence of the two causes with occurrences and nonoccurrences of the outcome. White (2008) proposed that such judgements could be predicted by a weighted averaging model integrating these kinds of contingency information. The weights in the model are derived from the hypothesis that causal judgements seek to meet two main aims, accounting for occurrences of the outcome and estimating the strengths of the causes. Here it is shown that the model can explain many but not all relevant published findings. The remainder can be explained by reasoning about interactions between the two causes, by scenario-specific effects, and by variations in cell weight depending on quantity of available information. An experiment is reported that supports this argument. The review and experimental results support the case for a cognitive model of causal judgement in which different kinds of contingency information are utilised to satisfy particular aims of the judgement process.

Keywords:

• Causal candidates
• Causal judgement
• Computational model

Notes

¹The Simpson's condition was named after Simpson's paradox. Two samples, A and B, can be divided into halves of unequal size, A1 and A2 and B1 and B2, such that the probability of an outcome occurring within A1 is greater than the probability of the outcome occurring in B1, the probability of the outcome occurring in A2 is greater than the probability of the outcome occurring in B2, but the overall probability of the outcome occurring is greater in B than in A. Spellman et al. (2001) provided an example in terms of baseball batting averages: A1 = 0.4 (4/10) and B1 = 0.3 (30/100); A2 = .25 (25/100) and B2 = .2 (2/10). Overall A = .264 (29/110) and B = .291 (32/110). Note the unequal sample sizes in each half: This is what makes the paradox possible (Spellman, 1996b). The Simpson's condition is not, strictly speaking, a case of Simpson's paradox: It is just a case where the conditional and unconditional contingencies for a cause have opposite signs.

²There have been some attempts to use different measures of causal judgement in other areas of the literature. Buehner, Cheng, and Clifford (2003) asked their participants to estimate “how many out of 100 people who did not have headaches would have a headache if given the medicine”. Comparisons between this measure and the kinds of measures used in the studies reviewed here would undoubtedly be enlightening, but it is not clear that it is a measure of causal judgement at all: People could answer the question by a simple empirical generalisation from the pattern of contingency detected in the stimulus materials, without an intervening causal judgement being made.