Making just school assignments

An assignment mechanism that eliminates justified envy is typically interpreted as being fair. It is well known that it is impossible for a mechanism to be strategyproof, Pareto efficient, and eliminate justified envy, but it is unknown what the strongest notion of fairness is that is achievable by a strategyproof and efficiency mechanism. We define an assignment to be unjust if a student i is not assigned to a school a that she prefers to her own assignment, i has higher priority at a than one of the students assigned to a, and it is possible to assign i to a without harming any of the students ranked higher at a than i. We prove that Top Trading Cycles is the unique mechanism that is strategyproof, efficient, and just. In this sense, Top Trading Cycles is the most fair among strategyproof and efficient mechanisms; any stronger notion notion of fairness is either satisfied by Top Trading †North Carolina State University. Email address: thayer [email protected]. I am grateful to Umut Dur and Melinda Morrill for their helpful comments.