  In many countries and institutions around the world, the hiring of workers is
made through open competitions. In them, candidates take tests and are ranked
based on scores in exams and other predetermined criteria. Those who satisfy
some eligibility criteria are made available for hiring from 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. When the scores are the
only criterion for selection, the procedure satisfies desired fairness and
independence properties. We show that when affirmative action policies are
introduced, the established methods of reserves and procedures used in Brazil,
France, and Australia, fail to satisfy those properties. We then present a new
rule, which we show to be the unique rule that extends static notions of
fairness to problems with multiple rounds while satisfying aggregation
independence, a consistency requirement. Finally, we show that if multiple
institutions hire workers from a single pool, even minor consistency
requirements are incompatible with variations in the institutions' rules.
