The structure of priority in the school choice problem

In a school choice problem each school has a priority ordering over the set of students. These priority orderings depend on criteria such as whether a student lives within walking distance or has a sibling already at the school. I argue that by including just the priority orderings in the problem, and not the criteria themselves, we lose important information. More particularly, the priority orderings fail to capture important aspects of the information from which they are derived when a student may satisfy a given criterion across multiple schools. This loss of information results in mechanisms that discriminate between students in ways that are not easy to justify. I propose an extended formulation of the school choice problem wherein a “priority matrix”, indicating which criteria are satisfied by each student-school pair, replaces the usual profile of priority orderings.