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

False Consensus, Information Theory, and Prediction Markets