Partitive Formulation of Information in Probabilistic Problems: Beyond Heuristics and Frequency Format Explanations

I propose a simple theory on the use of base rate according to which neither heuristic nor frequentist factors underlie demonstrations of the occurrence or the elimination of the base-rate fallacy. According to this view, what is crucial for the occurrence or elimination of the base-rate fallacy is the absence or presence, respectively, of what can be called a partitive formulation (Macchi, 1995) of the conditional likelihood datum. A partitive formulation defines the set of which the numerical datum is a part (in terms of percentages or frequencies) by referring to the likelihood datum relative to the base rate information. The predictive power of this hypothesis is shown by comparing responses to different versions of problems containing the same implied natural heuristic principles and supplied data, but which differ in the way the information is presented (partitive vs nonpartitive). Whether probabilistic or frequentist, the partitive versions lead to an almost complete elimination of the bias which remains when nonpartitive versions are used. On the basis of these experimental results, the paper includes a critical discussion of heuristic, frequentist, and mental models theories.