Replication data for: What's the Matter with Tie-Breaking? Improving Efficiency in School Choice

In several school choice districts in the United States, the student proposing deferred acceptance algorithm is applied after indifferences in priority orders are broken in some exogenous way. Although such a tie-breaking procedure preserves stability, it adversely affects the welfare of the students since it introduces artificial stability constraints. Our main finding is a polynomial-time algorithm for the computation of a student-optimal stable matching when priorities are weak. The idea behind our construction relies on a new notion which we call a stable improvement cycle. We also investigate the strategic properties of the student-optimal stable mechanism.

在美国多个择校学区中，当优先级顺序存在无差异时，需通过外生方式完成破局后，方可应用学生提议的延迟接受算法（student proposing deferred acceptance algorithm）。尽管此类破平局程序能够保留匹配的稳定性，但会引入人为的稳定性约束，进而对学生的福利造成不利影响。本文的核心研究发现为：针对优先级偏弱的场景，可设计一种多项式时间算法，用于求解学生最优稳定匹配（student-optimal stable matching）。该算法的设计思路依托于一个全新的概念——我们将其命名为稳定改进环（stable improvement cycle）。此外，本文还对学生最优稳定机制（student-optimal stable mechanism）的策略性质展开了研究。