Assigning Doctors to Rural Hospitals: Redesigning Colombia's Compulsory Social Service

Abstract We study many-to-one matching problems where doctors have strict preferences over hospitals, hospitals have strict preferences over sets of doctors, and the law assigns priorities to hospitals over doctors. A mechanism assigns a matching between doctors and hospitals. We are interested in mechanisms that respect priority, are efficient, are immune to strategic behavior, and minimize unfilled positions. We show that the lottery-based mechanisms used in Colombia in 2012--2013 satisfy none of these desirable properties. We then consider three mechanisms proposed in the literature: the deferred acceptance mechanism, the immediate acceptance mechanism (also known as the Boston mechanism), and the top trading cycle mechanism, and we explore different versions of efficiency, namely doctor-efficiency and priority-constrained efficiency.We find that all three mechanisms are priority-constrained efficient and minimize unfilled positions. The deferred acceptance mechanism is the only one of the three that respects priority, and it is strategy-proof, although it is neither doctor-efficient nor efficient. The top trading cycle mechanism and the immediate acceptance mechanism are doctor-efficient but do not respect priority; the top trading cycle mechanism is strategy-proof while the immediate acceptance mechanism is not. Finally, under the deferred acceptance and top trading cycle mechanisms---but not under the immediate acceptance mechanism---no doctor can obtain exemption from the compulsory service by misreporting. JEL Classication: C78; D47; D63; I18