The Bayesian logic of frequency-based conjunction fallacies

• Verfasst von: Sydow, Momme von [VerfasserIn]
• Titel: The Bayesian logic of frequency-based conjunction fallacies
• Verf.angabe: Momme von Sydow
• E-Jahr: 2011
• Jahr: 2 March 2011
• Umfang: 21 S.
• Fussnoten: Gesehen am 16.12.2022
• Titel Quelle: Enthalten in: Journal of mathematical psychology
• Ort Quelle: Orlando, Fla. : Academic Press, 1964
• Jahr Quelle: 2011
• Band/Heft Quelle: 55(2011), 2 vom: Apr., Seite 119-139
• ISSN Quelle: 0022-2496
• DOI: doi:10.1016/j.jmp.2010.12.001
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Bayesian models
• Sach-SW: Conjunction fallacy
• Sach-SW: Inductive logic
• Sach-SW: Paradoxes of predication
• Sach-SW: Probability judgments
• Sach-SW: Rationality
• K10plus-PPN: 1827603569

Abstract

An inductive, pattern-sensitive Bayesian logic (BL) is proposed as a normative and descriptive model for probability judgments about hypotheses involving probabilistic logical connectives. The model explains a specific class of frequency-based conjunction fallacies (CFs). It is suggested that the pattern probabilities calculated by BL may serve as a criterion of noisy-logical predication, resolving some paradoxes of predication. The model is developed for frequency information in 2×2 contingency tables. According to standard probability theory, a violation of the conjunction rule, P(A)≥P(A∧B) (e.g., P(ravens are black) ≥ P(ravens are black AND they can fly)), is always a fallacy. A frequentist interpretation of probability has exculpated participants from committing CFs when one is concerned with single events. Here a pattern-based Bayesian interpretation of probabilities of (noisy) dyadic logical predications is elaborated, predicting frequency-based but rational ‘CFs’. BL formalizes the probabilities of logical patterns, integrating over noise levels. BL, for instance, predicts double CFs, differential sample-size effects, and pattern sensitivity. Three experiments provide a first corroboration that BL is also an adequate empirical model to predict logical probability judgments based on 2×2 contingency tables. BL may shed light on the more general rationality debate.