Can Bayes' rule be justified by cognitive rationality principles?
The authors state that Bayes' rule (B.r.) has not yet received a clear epistemic justification based on subjective probabilities as true degrees of belief and points out three drawbacks: -- B.r. is not grounded on axioms which express cognitive rationality principles followed by the actor in any type of belief change; -- B.r. is not related to a precise epistemic context where it is assumed to adequately apply; -- B.r. cannot be used in situations where the message contradicts the initial belief, i.e. has zero prior probability. In order to overcome the three drawbacks, the authors trie to justify some families of change rules by a complete system of axioms reflecting principles of cognitive rationality. In the first part of the paper change axioms for both revising and updating contexts of change are considered. Set-theoretic axioms are recalled (Section 1.1), from which weak probabilistic axioms are then derived (Section 1.2); finally, strong probabilistic axioms extending the spirit of weak ones to a numerical framework are proposed and discussed (Section 1.3). The second part of the paper deals with change rules obtained by representation theorems for both contexts. Set-theoretic rules are recalled (Section 2.1), followed by probabilistic rules obtained with weak axioms (Section 2.2) and strong ones (Section 2.3).
scientific article; zbMATH DE number 1902309