The Strength of Conjunctive Explanations
Leddo, Abelson, and Gross (1984) reported two studies in which people rated conjunctions of two reasons as more likely explanations of event scenario outcomes than one or both of their component explanations even though objectively, the probability of a conjunction of two explanations can never exceed the probability of either of its component explanations. They interpreted this finding, "the conjunction effect," to mean that in general, conjunctive explanations are more persuasive than single explanations. The present article examines the results of those two studies plus four other studies in which conjunction effects occurred to find a mathematical model that can predict the conjoint explanation probability ratings from the probability ratings of their components. Several different models were evaluated according to two criteria: the number of parameters fitted and the multiple R of the model. The finding is that across all explanation triples (the conjoint explanation and its two component explanations), the relationship between the conjoint explanation probability ratings and their corresponding component ratings can best be expressed by the following formula: C = 1.15 G, where C is the conjoint explanation probability rating and G is the geometric mean of the component explanation probability ratings. This formula has a multiple R of .89, suggesting that this relationship is quite lawful. It is noted that finding the value ('conjunction coefficient') by which to multiply the geometric mean of the component ratings to predict the conjoint rating can serve as a measure of how well the component explanations combine or how compatible they are with each other in the given context. Similarly, comparing conjunction coefficients across several pairs of explanations can serve as a measure of the relative compatibility of different pairs of explanations. Implications of the conjunction coefficient model for the representativeness heuristic, the discounting principle, and the process of conjoint explanation are discussed.