We study dominant strategy implementation in the compromise setting of Borgers and Postl (2006), in which two agents have to choose one of three mutually exclusive alternatives. The agents' ordinal rankings of these three alternatives are commonly known among them, and they are diametrically opposed to each other. We study the problem of an arbitrator who has to decide whether to implement one of the agents' favourite alternatives, or whether to choose the compromise, by which we mean the alternative that they both rank second. For the class of binary decision rules, i.e. decision rules for which the probability of implementing the compromise is either 0 or 1, we characterize all decision rules that are implementable in dominant strategies. We also discuss some welfare properties of dominant strategy implementable decision rules.
