标题： 虚假共识，信息论和预测市场 显示英文标题

标题： False Consensus, Information Theory, and Prediction Markets

摘要： 我们研究一个设定，其中具有共同先验的贝叶斯代理人拥有与事件结果相关的私有信息，并依次做出与他们的信息相关的公开声明。 我们的主要结果表明，当代理人的私有信息在事件结果条件下是独立的，且代理人在结果上有相似的信念时，他们的信息会被聚合。 也就是说，不存在虚假共识。 我们的主要结果基于一个自然的信息理论框架，证明过程较为简短。 该框架的一个关键要素是“交互信息”的符号与人们信息价值的超加性/次加性性质之间的等价性。 这为交互信息提供了一个直观的解释和一个有趣的运用，交互信息衡量了三个随机变量之间共享的信息量。 我们通过在这个框架内重新证明两个额外的结果来展示这个信息理论框架的力量：1）当代理人在轮换方式下宣布（摘要）信念时，代理人的意见会迅速达成一致 [Aaronson 2005]；2）[Chen 等人 2010] 关于预测市场代理人何时应发布信息以最大化其报酬的结果。 我们还通过证明揭示信息的期望奖励是所揭示信息的条件互信息，来解释这个信息理论框架和上述结果在预测市场中的意义。 显示英文摘要

摘要： 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.