Many countries around the world, including Korea, use the school choice lottery system. However, this method has a problem in that many students are assigned to less-preferred schools based on the lottery results. In addition, the task of finding a good assignment with ties often has a time complexity of NP, making it a very difficult problem to improve the quality of the assignment. In this paper, we prove that the problem of finding a stable matching that maximizes the student-oriented preference utility in a two-sided market with one-sided preference can be solved in polynomial time, and we verify through experiments that the quality of assignment is improved. The main contributions of this paper are as follows. We found that stable student-oriented allocation in a two-sided market with one-sided preferences is the same as stable allocation in a two-sided market with symmetric preferences. In addition, we defined a method to quantify the quality of allocation from a preference utilitarian perspective. Based on the above two, it was proven that the problem of finding a stable match that maximizes the preference utility in a two-sided market with homogeneous preferences can be reduced to an allocation problem. In this paper, through an experiment, we quantitatively verified that optimal student assignment assigns more students to schools of higher preference, even in situations where many students are assigned to schools of low preference using the existing assignment method.

翻译：包括韩国在内的全球诸多国家采用学校择校抽签制度。然而，该方法存在一个缺陷：大量学生因抽签结果被分配到偏好较低的学校。此外，在存在平局的情况下寻找优质分配方案通常具有NP时间复杂度，这使得提升分配质量成为极具挑战性的难题。本文证明，在具有单边偏好的双边市场中，求解最大化学生导向偏好效用的稳定匹配问题可在多项式时间内完成，并通过实验验证了分配质量的提升效果。本文的主要贡献如下：研究发现，在单边偏好双边市场中，基于学生导向的稳定分配与对称偏好双边市场中的稳定分配具有等价性；此外，我们定义了一种从偏好功利主义视角量化分配质量的方法。基于上述两点，我们证明了在具有同质偏好的双边市场中寻找最大化偏好效用的稳定匹配问题可归约为分配问题。通过实验，本文定量验证了：即使现有分配方法导致大量学生被分配到低偏好学校的情况下，最优学生分配方案仍能将更多学生分配到高偏好学校。