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Bridging Bayesian Probability and AGM Revision via Stability Principles
March 3, 2014 @ 1:30 pm - April 1, 2014 @ 3:30 pm
(joint work with Alexandru Baltag)
This talk concerns the relationship between probabilistic (Bayesian) and qualitative (AGM-based) models of belief dynamics. I address the question of how AGM belief revision operators can be related to Bayesian conditioning, in order to flesh out some (in)compatibilities between the Bayesian and AGM-based formalisms.
This is done by analysing the behaviour of acceptance rules, which map probabilistic credal states to qualitative representations of belief. Given an acceptance rule, the ideal of compatibility between Bayesian conditioning and qualitative revision is embodied by the tracking property, which imposes a commutativity requirement to ensure that conditioning and revision agree modulo the acceptance map.
I focus on an acceptance rule based on the notion of stably high probability, due to Leitgeb. As a consequence of a 'No-Go' theorem by Lin & Kelly, Leitgeb's rule does not allow AGM revision to track conditioning. Nonetheless, given this rule's inherent attractiveness as an acceptance principle and its close connection to AGM revision, I consider some ways in which one may circumvent the No-Go Theorem and use the rule so as to approximate agreement between AGM and Bayesian conditioning.
I show that one rather natural such method – threshold-raising – fails, which poses some difficulties for the 'peace project' between Bayesian and AGM-compliant operators. However, another interesting connection exists: I show that there is a sense in which AGM revision derives from (1) Leitgeb's rule, (2) Bayesian conditioning, and (3) a version of the maximum entropy principle. This suggests that one could study qualitative revision operators as special cases of Bayesian reasoning which naturally arise in situations of information loss or incomplete probabilistic information.