On the Consistency among Prior, Posteriors, and Information Sets (Extended Abstract)

Satoshi Fukuda
(Department of Decision Sciences and IGIER, Bocconi University)

This paper studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency conditions as: (i) the information sets, without any assumption, almost surely form a partition; and (ii) the posterior at a state is equal to the Bayes conditional probability given the corresponding information set. Implications are as follows. First, each posterior is uniquely determined. Second, qualitative belief reduces to fully introspective knowledge in a ``standard'' environment. Thus, a care must be taken when one studies non-veridical belief or non-introspective knowledge. Third, an information partition compatible with the consistency conditions is uniquely determined by the posteriors. Fourth, qualitative and probability-one beliefs satisfy truth axiom almost surely. The paper also sheds light on how the additivity of the posteriors yields negative introspective properties of beliefs.

In Lawrence S. Moss: Proceedings Seventeenth Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2019), Toulouse, France, 17-19 July 2019, Electronic Proceedings in Theoretical Computer Science 297, pp. 189–205.
Published: 19th July 2019.

ArXived at: https://dx.doi.org/10.4204/EPTCS.297.13 bibtex PDF
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