  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.
