Hiring from a pool of workers

We consider the hiring of public sector workers through legislated rules and exam-based rankings, as is done in many countries and institutions around the world. In them, workers take tests and are ranked based on scores in exams and other pre-determined criteria, and those who satisfy some eligibility criteria are made available for hiring in a "pool of workers." In each of an ex-ante unknown number of rounds, vacancies are announced and workers are then hired from that pool. We show that when the scores are the only criterion for selection, the procedure satisfies desired fairness and independence properties. We show, with the aid of details of procedures used in Brazil, France and Australia, that when compositional objectives are introduced, such as affirmative action policies, both the procedures used in the field and in the literature fail to satisfy those properties. We then present a new rule, which we show to be the unique rule that satisfies those properties. Finally, we show that if multiple institutions hire workers from a single pool, even minor consistency requirements are incompatible with compositional objectives.