Abstract
We propose mechanisms for two parties with potentially conflicting objectives to jointly select a predetermined number of candidates to occupy decision-making positions. Two leading examples of these situations are: i) the selection of an arbitrator panel by two conflicting firms, and ii) the bipartisan coalition's selection of a set of judges to occupy court vacancies. We analyze the efficiency, fairness, and simplicity of equilibrium outcomes in strategic games induced by these mechanisms. Their effectiveness hinges on the parties' preferences over the sets containing the required number of the candidates to be chosen.