The Bayesian logic of frequency-based conjunction fallacies
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 pa...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2 March 2011
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| In: |
Journal of mathematical psychology
Year: 2011, Volume: 55, Issue: 2, Pages: 119-139 |
| ISSN: | 0022-2496 |
| DOI: | 10.1016/j.jmp.2010.12.001 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jmp.2010.12.001 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0022249610001422 
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| Author Notes: | Momme von Sydow |
| Summary: | 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. |
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| Item Description: | Gesehen am 16.12.2022 |
| Physical Description: | Online Resource |
| ISSN: | 0022-2496 |
| DOI: | 10.1016/j.jmp.2010.12.001 |