We study information aggregation with a decision maker aggregating binary recommendations from symmetric agents. Each agent's recommendation depends on her private information about a hidden state. While the decision maker knows the prior distribution over states and the marginal distribution of each agent's recommendation, the recommendations are adversarially-correlated. The decision maker's goal is choosing a robustly-optimal aggregation rule. We prove that for a large number of agents, for the three standard robustness paradigms - minimax, regret and approximation ratio - the unique optimal aggregation rule is random dictator. We further characterize the minimal regret for any agents' number through concavification.

翻译：我们研究了一个决策者聚合来自对称代理的二元推荐的信息聚合问题。每个代理的推荐取决于其关于隐藏状态的私有信息。尽管决策者知道状态的先验分布以及每个代理推荐意见的边际分布，但这些推荐意见是敌意相关的。决策者的目标是选择一种稳健最优的聚合规则。我们证明，对于大量代理，在三种标准稳健性范式——极小化极大、遗憾和近似比——下，唯一的最优聚合规则是随机独裁。我们进一步通过凹化方法刻画了任意代理数量下的最小遗憾。