Universally Robust Information Aggregation for Binary Decisions

We study a setting with a decision maker making a binary decision by aggregating information from symmetric agents. Each agent provides the decision maker a recommendation depending on her private signal about the hidden state. We assume that agents are truthful - an agent recommends guessing the more likely state based on her information. This assumption is natural if the agents are unaware of how the decision-maker will aggregate their recommendations. While the decision maker has a prior distribution over the hidden state and knows the marginal distribution of each agent's private signal, the correlation between these signals is chosen adversarially. The decision maker's goal is choosing an information aggregation rule that is robustly optimal.