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Mediation is an alternative dispute resolution method, which has gained increasing popularity over the last few decades and become a multi-million dollar industry. When two or more parties are in a disagreement, they can take the case to a court and let the judge make a binding final decision. Alternatively, the disputing parties can get assistance from an experienced, neutral third party, i.e., a mediator, who facilitates the negotiation and help them voluntarily reach an agreement short of litigation. The emphasis in mediation is not upon who is right or wrong, but rather on exploring mutually satisfactory solutions. Employment disputes, patent/copyright violations, construction disputes, and family disputes are some of the most common mediated disputes. The rising popularity of mediation is often attributed to the increasing workload of courts, its cost effectiveness and speed relative to litigation, and disputants’ desire to have control over the final decision. Many traditional "cardinal" settings of bargaining and mechanism design, starting with the seminal work of Myerson and Satterhwaite (1983), have shown the incompatibility between efficiency and incentives, even in Bayesian sense. This paper uses an "ordinal" market/mechanism design approach, where the mediator seeks a resolution over (at least) two issues in which negotiators have diametrically opposed rankings over the alternatives. Each negotiator has private information about her own ranking of the outside option, e.g., the point beyond which the negotiator would rather take the case to the court. We construct a simple theoretical framework that is rich and practical enough allowing for optimal mechanisms that the mediators can use for efficient resolution of disputes. We propose and characterize the class of strategy-proof, efficient, and individually rational mediation mechanisms. A central member of this class, the "constrain-and-choose" mechanism stands out as the unique strategy-proof, efficient, and individually rational mechanism that minimizes rank variance. We also provide analogous mechanisms when the issues consist of a continuum of alternatives.
