Abstract
The justification of Bayes' rule by cognitive rationality principles is undertaken by extending the propositional axiom systems usually proposed in two contexts of belief change: revising and updating. Probabilistic belief change axioms are introduced, either by direct transcription of the set-theoretic ones, or in a stronger way but nevertheless in the spirit of the underlying propositional principles. Weak revising axioms are shown to be satisfied by a General Conditioning rule, extending Bayes' rule but also compatible with others, and weak updating axioms by a General Imaging rule, extending Lewis' rule. Strong axioms (equivalent to the Miller–Popper axiom system) are necessary to justify Bayes' rule in a revising context, and justify in fact an extended Bayes' rule which applies, even if the message has zero probability.
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Walliser, B., Zwirn, D. Can Bayes' Rule be Justified by Cognitive Rationality Principles?. Theory and Decision 53, 95–135 (2002). https://doi.org/10.1023/A:1021227106744
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DOI: https://doi.org/10.1023/A:1021227106744