Can Bayes' Rule be Justified by Cognitive Rationality Principles?

Theory and Decision 53 (2):95-135 (2002)
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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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Denis Zwirn
École Polytechnique

References found in this work

Probability, Frequency, and Reasonable Expectation.Richard T. Cox - 1946 - American Journal of Physics 14 (2):1-13.
Bayesian conditionalisation and the principle of minimum information.P. M. Williams - 1980 - British Journal for the Philosophy of Science 31 (2):131-144.
Imaging and conditionalization.Peter Gardenfors - 1982 - Journal of Philosophy 79 (12):747-760.
Five faces of minimality.David Makinson - 1993 - Studia Logica 52 (3):339 - 379.

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