Designing Rules for Choosing a Winner in a Debate

We consider settings where an uninformed principal must hear arguments from two better-informed agents, corresponding to two possible courses of action that they argue for. The arguments are verifiable in the sense that the true state of the world restricts the arguments that can be made by the agents. Each agent simply wants to be chosen as the winner and does so strategically based on the rule set by the principal. How should the principal design the rule to choose the better action? We provide a formal framework for answering this question, exhibit some basic properties of it, study the computational problems of evaluating and optimizing the principal's policy, and provide key error bounds.