We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs in the population are feasible. We provide a necessary and sufficient condition for feasibility. We apply this result in several domains. First, we study the problem of maximizing the polarization of beliefs in a population. Second, we provide a characterization of the feasible agent-symmetric product distributions of posteriors. Finally, we study an instance of a private Bayesian persuasion problem and provide a clean formula for the sender's optimal value.
翻译：我们认为,巴伊西亚的代理人在某个有限的国家空间上有着共同的先天性,每个代理人都接触到一些关于国家的信息。我们询问,在人口中后人信仰的经验分布方面,哪些分布是可行的。我们为可行性提供了必要和充分的条件。我们把这一结果应用于几个领域。首先,我们研究在人口中使信仰的两极分化最大化的问题。第二,我们对后人可行的代理对称产品分布进行定性。最后,我们研究一个私人巴伊西亚人的说服问题,并为发送者的最佳价值提供一个干净的公式。
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