We provide a school choice model where the student priority orders for schools are allowed not to be total. We introduce a class of algorithms, each of which derives a student optimal stable matching once we have an initial stable matching, when the priorities are represented by partial orders. Since a method to derive a stable matching exists when the priorities are partial orders, we can use it to derive a student optimal stable matching. Moreover, we show that any student optimal stable matchings that Pareto dominate the starting stable one are obtained via an algorithm within this class. For the problem of improving efficiency by allowing some priorities to be violated, the algorithms can also be applied, with a weaker assumption on the violations than in the previous study. Finally, we suggest some specific rules of priorities that can be introduced by weakening the requirement of total ordering.

我们提供了一个学校选择模型，其中不允许总计学生的学校优先顺序。我们引入一类算法，当优先级由偏序表示时，一旦有了初始稳定匹配，每种算法都会得出学生的最佳稳定匹配。由于当优先级为部分订单时，存在一种推导稳定匹配的方法，因此我们可以使用它来推导学生的最佳稳定匹配。此外，我们表明，通过该类中的算法，可以获得帕累托支配开始稳定的任何学生最佳稳定匹配。对于通过允许违反某些优先级来提高效率的问题，也可以使用算法，对违规的假设要比以前的研究要弱。最后，