Hiring from a Pool of Workers

Abstract

We consider he hiring of workers through legislated rules and exam-based rankings. Workers take tests and are ranked based on scores in exams and other pre-determined criteria. Workers who satisfy some eligibility criteria are made available for hiring in a pool of workers. Vacancies are announced in rounds and the total number of vacancies is ex-ante unknown. In each round, a given number of workers are selected to fill the announced positions, based on a selection rule, typically specified by legislation. When the scores are the only criterion for selection, the procedure satisfies desired fairness and independence properties. We show, however, that when compositional objectives are introduced, such as the quotas for minorities and people with disabilities observed in countries such as Brazil and France, both the procedures used in the field and in the literature fail to satisfy those properties. We present the sequential adjusted minority reserves rule, which is the unique rule that satisfies the desired properties. Finally, we show that if multiple institutions hire workers from a single pool, even minor consistency requirements are incompatible with compositional objectives.