Conditional Probabilities, Potential Surprise, and the Conjunction Fallacy

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Abstract
Tversky and Kahneman (1983) found that a relationship of positive conditional dependence between the components of a conjunction of two events increases the prevalence of the conjunction fallacy. Consistent with this finding, the results of two experiments reveal that dependence leads to higher estimates for the conjunctive probability and a higher incidence of the fallacy. However, contrary to the theoretical account proposed by Tversky and Kahneman, the actual magnitude of the conditional relationship does not directly affect the extent of the fallacy; all that is necessary is for a positive conditional relationship to exist. The pattern of results obtained can be accounted for in terms of Shackle's (1969) “potential surprise” theory of subjective probability. Surprise theory predicts that the impact of the conditional event will be at its maximum where the relationship is a negative one. Tversky and Kahneman's model, on the other hand, predicts the maximum effect when the relationship is positive. In all 12 scenarios tested, multiple regression analysis revealed that the standardized beta weight associated with the conditional event was greater when the relationship was a negative one. Thus the outcome was supportive of the surprise model rather than Tversky and Kahneman's account.