Pattern Probabilities for Non-Dichotomous Events: A New Rational Contribution to the Conjunction Fallacy Debate

This paper analyzes probability judgments about properties that can take multiple values (i.e., monadic polytomous events). It extends previous work on pattern-based deviations from standard (extensional) probabilities. Pattern-probabilities are formalized in Bayesian Logic (BL) and should be applicable when testing the overall adequacy of alternative logical hypotheses while allowing for exceptions. BL systematically predicts ‘conjunction fallacies’ (CFs) and, more generally, ‘inclusion fallacies’ (IFs), when a subset is deemed more probable than its superset. BL formalizes a fit between data and explanatory noisy-logical patterns and was supported in previous experiments on dyadic logical connectives with two dichotomous events. Here BL is extended to monadic prediction with several subclasses. BL may for instance predict Ppattern(A) > Ppattern(non-A) even though f(A) < f(non-A), given that non-A has more subclasses than A. Two experiments using material from the Linda paradigm corroborate a pattern approach and rule out confirmation as an alternative explanation.