  We study a setting where Bayesian agents with a common prior have private
information related to an event's outcome and sequentially make public
announcements relating to their information. Our main result shows that when
agents' private information is independent conditioning on the event's outcome
whenever agents have similar beliefs about the outcome, their information is
aggregated. That is, there is no false consensus.
  Our main result has a short proof based on a natural information theoretic
framework. A key ingredient of the framework is the equivalence between the
sign of the ``interaction information'' and a super/sub-additive property of
the value of people's information. This provides an intuitive interpretation
and an interesting application of the interaction information, which measures
the amount of information shared by three random variables.
  We illustrate the power of this information theoretic framework by reproving
two additional results within it: 1) that agents quickly agree when announcing
(summaries of) beliefs in round robin fashion [Aaronson 2005]; and 2) results
from [Chen et al 2010] on when prediction market agents should release
information to maximize their payment. We also interpret the information
theoretic framework and the above results in prediction markets by proving that
the expected reward of revealing information is the conditional mutual
information of the information revealed.
