A Random Dictator Is All You Need

Arieli, Itai; Babichenko, Yakov; Talgam-Cohen, Inbal; Zabarnyi, Konstantin

doi:10.1257/mic.20230255

Abstract

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.

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A Random Dictator Is All You Need

Abstract

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