  We study the set of possible joint posterior belief distributions of a group
of agents who share a common prior regarding a binary state, and who observe
some information structure. For two agents we introduce a quantitative version
of Aumann's Agreement Theorem, and show that it is equivalent to a
characterization of feasible distributions due to Dawid et al. (1995). For any
number of agents, we characterize feasible distributions in terms of a
"no-trade" condition. We use these characterizations to study information
structures with independent posteriors. We also study persuasion problems with
multiple receivers, exploring the extreme feasible distributions.
