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arXiv · 2302.03667

A Random Dictator Is All You Need

Itai Arieli·Yakov Babichenko·Inbal Talgam-Cohen·Konstantin Zabarnyi
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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 - 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.

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Itai Arieli, Yakov Babichenko, Inbal Talgam-Cohen, Konstantin Zabarnyi. 2023-02-07. A Random Dictator Is All You Need. https://arxiv.org/abs/2302.03667

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