智能彩票在校园选择中的应用：事前帕累托改进与事后稳定性
Smart Lotteries in School Choice: Ex-ante Pareto-Improvement with Ex-post Stability
AI总结：
本文提出了一种智能彩票机制，通过事前改进概率分配并保持事后稳定性，实现校园选择中的帕累托改进。
摘要：
在典型的校园选择应用中，学生对学校有严格偏好，而学校则基于距离和已注册的同龄人对申请人有粗略的优先级排序。中央招生机制的结果通常通过延迟接受（DA）算法和随机打破平局来获得。因此，该机制的每一个可能结果都是粗略优先级的稳定解，这些解将以一定概率出现。这暗示了一种概率性分配，其中每个学生-学校对的录取概率被指定。在本文中，我们提出了一种新的效率提升的稳定'智能彩票'机制。我们的目标是通过随机支配的意义在事前改进概率分配，同时确保改进的随机匹配仍然是事后稳定的，即可以分解为原粗略优先级的稳定匹配。因此，这种智能彩票机制可以为任何基数效用提供清晰的期望帕累托改进，优于标准DA加彩票解，而不会牺牲最终结果的稳定性。我们证明尽管底层的计算问题是NP难的，但我们可以通过使用整数规划与列生成等先进优化技术来解决这个问题。我们在生成和真实实例上进行了计算实验。我们的结果表明，通过我们的机制获得的福利收益显著大于标准方法在打破平局后实现的效率改进预期收益。
英文摘要：
In school choice, students typically have strict preferences over the schools while the schools have coarse priorities over the students based on their distance and their enrolled siblings. The outcome of a centralized admission mechanism is then usually obtained by the Deferred Acceptance (DA) algorithm with random tie-breaking. Therefore, every outcome of this mechanism that occurs with a positive probability is a stable solution for the coarse priorities. This implies a probabilistic assignment, specifying the admission probability for each student-school pair. In this paper, we propose a new efficiency-improving stable 'smart lottery' mechanism. We aim to improve the probabilistic assignment ex-ante in a stochastic dominance sense, while ensuring that the improved random matching is still ex-post stable, meaning that it can be decomposed into stable matchings regarding the original coarse priorities. Therefore, this smart lottery mechanism can provide a clear Pareto-improvement in expectation for any cardinal utilities compared to the standard DA with lottery solution, without sacrificing the stability of the final outcome. We show that although the underlying computational problem is NP-hard, we can solve the problem in practice by using column generation. Our computational results show that the welfare gains by our mechanism are substantially larger than the expected gains by standard methods that realize efficiency improvements after ties have already been broken. Additionally, we illustrate for real-world school choice data of Ghent (Belgium) that, while not theoretically guaranteed, our mechanism can Pareto-improve upon methods that improve upon DA but violate ex-post stability, such as Efficiency-Adjusted Deferred Acceptance.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
