Priority Design in Centralized Matching Markets
研究了在集中匹配市场中，如何将底层分数粗化为优先权等级，并证明在稳定匹配机制下，最优设计只需将每个对象的申请者分为最多三个无差异等级。
Abstract In many centralized matching markets, agents’ property rights over objects are derived from a coarse transformation of an underlying score. Prominent examples include the distance-based system employed by Boston Public Schools, where students who lived within a certain radius of each school were prioritized over all others, and the income-based system used in New York public housing allocation, where eligibility is determined by a sharp income cutoff. Motivated by this, we study how to optimally coarsen an underlying score. Our main result is that, for any continuous objective function and under stable matching mechanisms, the optimal design can be attained by splitting agents into at most three indifference classes for each object. We provide insights into this design problem in three applications: distance-based scores in Boston Public Schools, test-based scores for Chicago exam schools, and income-based scores in New York public housing allocation.