The Impossibility of Restricting Tradeable Priorities in School Assignment

E cient school assignments are made by allowing students to trade their priorities. However, a school board typically gives the highest priority at a school to students who have a sibling attending the school, and a school board might not want to allow a student to trade such a school-speci c priority. This paper addresses the following question: is it possible to design a strategy-proof trading mechanism where the designer can specify priorities that are not allowed to be traded? We demonstrate that it is impossible to restrict which priorities are traded and maintain minimal e ciency properties. Speci cally, we de ne a mechanism to be perfect if each agent is assigned her top choice whenever such an assignment is feasible. We show that even this minimal level of e ciency is incompatible with making some of the priorities untradeable. We also show that an agent's improvement in priorities may be punished by any non-wasteful, individually rational and mutually best mechanism which allows agents to trade only the tradeable priorities. JEL Classi cation: C78, D61, H75, I28