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.

翻译：我们研究一种环境,让拥有共同前位的巴伊西亚代理人拥有与事件结果有关的私人信息,并按顺序发布与其信息有关的公开信息。我们的主要结果显示,当代理人的私人信息在对结果有类似信仰时对事件结果有独立限制时,他们的信息是汇总的。也就是说,不存在虚假的共识。我们的主要结果有一个基于自然信息理论框架的简短证据。框架的一个关键要素是“互动信息”和“人民信息价值的超级/子补充属性”的信号之间的等值。这为互动信息提供了直观的解释和有趣的应用,该互动信息衡量三个随机变量共享的信息数量。我们通过在信息框架内调整两个额外结果来说明这一信息理论框架的力量:(1) 代理人在宣布(概述)轮式信仰时[Aaronson 2005年] 迅速达成一致;(2) 预测市场代理人应何时发布信息以最大限度地支付信息。我们还解释了信息理论框架和通过预测市场来显示的预期结果。