We study an information aggregation setting in which a decision maker makes an informed binary decision by merging together information from several symmetric agents. Each agent provides the decision maker with a recommendation, which depends on her information about the hidden state of nature. While the decision maker has a prior distribution over the hidden state and knows the marginal distribution of each agent's recommendation, the correlation between the recommendations is chosen adversarially. The decision maker's goal is to choose an information aggregation rule that is robustly optimal. We prove that for a sufficiently large number of agents, for the three standard robustness paradigms - minimax, regret and approximation ratio - the robustly-optimal aggregation rule is identical. Specifically, the optimal aggregation rule is the random dictator rule, which chooses an agent uniformly at random and adopts her recommendation. For a small number of agents, this result no longer holds - the random dictator rule can be suboptimal for minimizing the regret even for two agents. We further characterize the minimal regret for any number of agents through the notion of concavification, and demonstrate how to utilize this characterization in the case of two agents.

翻译：我们研究了一个信息聚合场景，在该场景中，决策者通过合并来自多个对称智能体的信息做出知情的二元决策。每个智能体根据其对隐藏自然状态的信息向决策者提供建议。虽然决策者拥有关于隐藏状态的先验分布，并知道每个智能体建议的边际分布，但建议之间的相关性是由对手选择的。决策者的目标是选择一个稳健最优的信息聚合规则。我们证明，当智能体数量足够大时，对于三种标准稳健性范式——极小极大、遗憾和近似比——稳健最优的聚合规则是相同的。具体而言，最优聚合规则是随机独裁规则，即均匀随机选择一个智能体并采纳其建议。对于少量智能体，这一结论不再成立——即使对于两个智能体，随机独裁规则在最小化遗憾方面也可能不是最优的。我们进一步通过凹化概念刻画了任意数量智能体下的最小遗憾，并展示了如何在两个智能体的情况下利用这一刻画。