Revising the school choice problem

In a school choice problem each school has a priority ordering over students. These priority orderings depend on criteria such as whether a student lives within walking distance or has a sibling already at the school. We argue that by including just the priority orderings in the problem, and not the criteria themselves, we lose crucial information. This loss of information results in mechanisms that discriminate between students in ways that are difficult to justify. We propose an alternative school choice problem and adaptations of the Gale-Shapley student optimal stable mechanism and the top trading cycles mechanism.