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  5. A Random Dictator Is All You Need

American Economic Journal:
Microeconomics

ISSN 1945-7669 (Print) | ISSN 1945-7685 (Online)

A Random Dictator Is All You Need

  • Itai Arieli
  • Yakov Babichenko
  • Inbal Talgam-Cohen
  • Konstantin Zabarnyi
American Economic Journal: Microeconomics (Forthcoming)

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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