Robust Aggregation of Correlated Information

Abstract: An agent makes decisions based on multiple sources of information. In isolation, each source is well understood, but their correlation is unknown. We study the agent's robustly optimal strategies -- those that give the best possible guaranteed payoff, even under the worst possible correlation. With two states and two actions, we show that a robustly optimal strategy uses a single information source, ignoring all others. In general decision problems, robustly optimal strategies combine multiple sources of information, but the number of information sources that are needed has a bound that only depends on the decision problem. These findings provide a new rationale for why information is ignored.