We investigate efficient and minimally unstable Pareto improvements over the deferred acceptance (DA) mechanism—a popular school choice mechanism that is stable but not efficient. We show that there is no Pareto improvement over the DA mechanism that is minimally unstable among efficient assignments when the stability comparison is based on counting the number of blocking pairs. Our main result characterizes the priority profiles for which there exists a Pareto improvement over the DA assignment that is minimally unstable among efficient assignments. We further consider an alternative natural stability comparison based on the set of blocking students who are involved in at least one blocking pair, show that the impossibilities remain, and characterize the possibility domain of priority profiles.

中文翻译：

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与延迟接受相比，帕累托改进最小化不稳定

我们研究了对延迟接受 (DA) 机制的有效且最小不稳定的帕累托改进——这是一种稳定但不高效的流行学校选择机制。我们表明，当稳定性比较基于计数阻塞对的数量时，在有效分配中最小不稳定的 DA 机制没有帕累托改进。我们的主要结果描述了优先级配置文件，其中存在对有效分配中最小不稳定的 DA 分配的帕累托改进。我们进一步考虑基于参与至少一个阻塞对的一组阻塞学生的替代自然稳定性比较，表明仍然存在不可能性，并描述优先级配置文件的可能性域。