We propose a new simple procedure called Population-Mean-Based Aggregation (PMBA) that enables a principal to "aggregate" information about an unknown state of the world from agents without understanding the information structure among them. PMBA only requires agents to communicate their beliefs about the state, and some agents to communicate their expectations of the population average belief. In a large population, for any finite number of possible states, and under weak assumptions on the information structure, allowing individual agents' beliefs to be misspecified, we show that PMBA infers the true state (in probability or almost surely under the stated conditions). We show how PMBA can be reinterpreted as a linear regression procedure, and how it can be used to aggregate information from a finite number of agents, allowing us to reuse existing results on inference in linear models. We conduct a novel experiment to show that the real-world performance of our procedure exceeds that of existing methods.

翻译：我们提出一种称为“基于总体均值的聚合”（PMBA）的新颖简单程序，该程序使委托人能够在无需理解代理人之间信息结构的情况下，从代理人处“聚合”关于世界未知状态的信息。PMBA 仅要求代理人传达其对状态的信念，并要求部分代理人传达其对总体平均信念的期望。在总体规模较大、可能状态数量有限且信息结构假设较弱（允许个体代理人信念存在错误指定）的情况下，我们证明 PMBA 能推断出真实状态（在所述条件下，依概率或几乎必然地）。我们展示了 PMBA 可被重新解释为一种线性回归程序，并可用于从有限数量的代理人处聚合信息，从而得以复用线性模型推断的现有成果。通过一项新颖实验，我们证明了该程序在实际应用中的表现优于现有方法。