A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. We show that, if beliefs given a union of two databases are a convex combination of beliefs given each of the databases, the...

A decision maker is asked to express her beliefs by assigning probabilities to certain possible states. We focus on the relationship between her database and her beliefs. We show that if beliefs given a union of two databases are a convex combination of beliefs given each of the databases, the...

Aumann has shown that agents who have a common prior cannot have common knowledge of their posteriors for event $E$ if these posteriors do not coincide. But given an event $E$, can the agents have posteriors with a common prior such that it is common knowledge that the posteriors for $E$...