A Random Dictator Is All You Need

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 (maximin, regret, and approximation ratio), the unique optimal aggregation rule is “random dictator.” We further characterize the minimal regret for any number of agents through concavification.