标题： 关于学校选择中部分优先级的扩展 显示英文标题

标题： On extensions of partial priorities in school choice

摘要： 我们考虑了一个学校选择匹配模型，在这个模型中，学校的优先级由二元关系表示，这些关系可能不是弱序的。我们关注的是这些二元关系的（全序）扩展。我们引入了一类算法来推导二元关系的一个扩展，并通过使用这一类来刻画它们。我们证明，如果这些二元关系是偏序，则对于每个基于这些二元关系的配置文件的稳定匹配，存在一个扩展使得该匹配也是稳定的。此外，如果根据帕累托占优，对于这些二元关系的配置文件存在多个稳定匹配，则存在一个扩展，使得所有这些匹配都是稳定的。我们提供了这些结果的若干应用。 显示英文摘要

摘要： We consider a school choice matching model where the priorities for schools are represented by binary relations that may not be weak order. We focus on the (total order) extensions of the binary relations. We introduce a class of algorithms to derive one of the extensions of a binary relation and characterize them by using the class. We show that if the binary relations are the partial orders, then for each stable matching for the profile of the binary relations, there is an extension for which it is also stable. Moreover, if there are multiple stable matchings for the profile of the binary relations that are ranked by Pareto dominance, there is an extension for which all of those matchings are stable. We provide several applications of these results.