Lottery mechanism design for school choice

A new centralized mechanism was introduced in New York City and Boston to assign students to public schools in district school-choice programs. This mechanism was advocated for its superior fairness property, besides others, over the mechanisms it replaced. In this paper, we introduce a new framework for investigating school-choice matching problems and two notions of fairness in lottery design, strong ex-ante stability and ex-ante stability. This framework generalizes known one-to-many two-sided and one-sided matching models. We first show that the new NYC/Boston mechanism fails to satisfy these fairness properties. We then propose two new mechanisms, the fractional deferred acceptance mechanism, which is ordinally Pareto dominant within the class of strongly ex-ante stable mechanisms, and the fractional deferred acceptance and trading mechanism which is constrained ordinally Pareto efficient within the class of exante stable mechanisms.