Is There a Monadic as well as a Dyadic Bayesian Logic? Two Logics Explaining Conjunction ‘Fallacies’

Momme von SydowUniversity of Heidelberg, Heidelberg, Germany

Abstract

Formal logic and probability theory are often considered the most fundamental norms of rational thought, but their application to psychological tasks has raised serious doubts about human rationality. A central finding is that people sometimes judge the probability of a conjunction to be higher than that of its conjuncts (conjunction fallacies, CFs). Bayesian logic (BL, von Sydow, 2011) formalizes subjective probabilities of noisy-logical explanatory patterns (pattern probabilities) instead of extensional probabilities (relative frequencies), and predicts a system of rational inclusion fallacies. This paper distinguishes a monadic from a dyadic pattern explanation of CFs; it tests two corresponding formalizations of BL (the former concerned with cells, the latter with marginals); and it models pattern probabilities in a novel way (based on acceptance thresholds). In an experiment we varied observed frequencies and formulations. The results deviate radically from narrow norms but they corroborate the idea of monadic and dyadic pattern probabilities.

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