Decisions are typically made by drawing on multiple sources of information, yet the correlation among these sources is often hard to assess. We study robustly optimal strategies—those that maximize the worst-case payoff guarantee across all correlation structures. With two states and two actions, the robustly optimal strategy is strikingly simple: use only the best information source and ignore the rest. With more actions, a robustly optimal strategy decomposes the problem into local comparisons and assigns each comparison to the source that is best at that comparison. With more states, the same specialization logic survives through a concavification characterization: the decision problem is decomposed into payoff-relevant components, and each component is assigned to its best source. These results offer a new rationale for why ignoring information can be optimal and highlight the benefit of using specialized information sources when correlations are ambiguous.

We propose a new notion of credibility for Bayesian persuasion problems. A disclosure policy is credible if the sender cannot profit from tampering with her messages while keeping the message distribution unchanged. We show that the credibility of a disclosure policy is equivalent to a cyclical monotonicity condition on the policy’s induced distribution over states and actions. We also characterize how credibility restricts the sender’s ability to persuade under different payoff structures. In particular, when the sender’s payoff is state independent, all disclosure policies are credible. We apply our results to the market for lemons and show that no useful information can be credibly disclosed by the seller.

The seller of an asset has the option to buy hard information about the value of the asset from an intermediary. The seller can then disclose this information before selling the asset in a competitive market. We study how the intermediary designs and sells hard information to robustly maximize the intermediary's revenue across all equilibria. Even though the intermediary could use an accurate test that reveals the asset’s value, we show that robust revenue maximization leads to a noisy test with a continuum of possible scores. In addition, the intermediary always charges the seller for disclosing the test score to the market, but not necessarily for running the test. This enables the intermediary to robustly appropriate a significant share of the surplus resulting from the asset sale.