A Random Dictator Is All You Need

TL;DR

This paper demonstrates that in a setting with symmetric agents providing binary recommendations based on private information, the optimal robust aggregation rule for a large number of agents is a simple random dictator, regardless of the robustness criterion.

Contribution

It establishes the uniqueness of the random dictator rule as the optimal aggregation method under multiple robustness paradigms in adversarially-correlated recommendation settings.

Findings

Random dictator is the unique optimal rule for large agent populations.

Optimal regret can be characterized through concavification.

The result holds across minimax, regret, and approximation ratio paradigms.

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.