Decision Rules for Experts with Opposing Interests

This paper studies optimal decision rules for a decision maker who can consult two experts in an environment without monetary payments. This extends the previous work by Holmström (1984) and Alonso and Matouschek (2008) who consider environments with one expert. In order to derive optimal decision rules, we prove a "constant-threat" result that states that any out-of-equilibrium pair of recommendations by the experts are punished with an action that is independent of their reports. A particular property of an optimal decision rule is that it is simple and constant for a large set of experts' preferences and distribution of their private information. Hence, it is robust in the sense that it is not affected by errors in specifying these features of the environment. By contrast, the constructions of optimal outcomes absent commitment or with only one expert are sensitive to model details.