In a school choice problem, each school has a priority ordering over the set of students. These orderings depend on criteria such as whether a student lives within walking distance or has a sibling at the school. A priority ordering provides a ranking of students but nothing more. I argue that this information is sufficient when priority is based on merit but not when priority is based on criteria such as walking distance. I propose an extended formulation of the problem wherein a ‘priority matrix’, indicating which criteria are satisfied by each student-school pair, replaces the usual priority orderings.

中文翻译：

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择校问题中的优先结构

在学校选择问题中，每所学校对学生集都有优先排序。这些排序取决于标准，例如学生是否住在步行距离内或在学校有兄弟姐妹。优先顺序提供了学生的排名，仅此而已。我认为，当优先级基于优点时，这些信息就足够了，但当优先级基于步行距离等标准时，这些信息就足够了。我提出了这个问题的扩展公式，其中一个“优先级矩阵”，指示每个学生-学校对满足哪些标准，取代了通常的优先级排序。