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

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