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

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

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

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

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

Oligarchy and soft incompleteness

The assumption that the social preference relation is complete is demanding. We distinguish between “hard” and “soft” incompleteness, and explore the social choice implications of the latter. Under soft incompleteness, social preferences can take values in the unit interval. We motivate interest in soft incompleteness by presenting a version of the strong Pareto rule that is suited to the context of a [0, 1]-valued social preference relation. Using a novel approach to the quasi-transitivity of this relation we prove a general oligarchy theorem. Our framework allows us to make a distinction between a “strong” and a “weak” oligarchy, and our theorem identifies when the oligarchy must be strong and when it can be weak. Weak oligarchy need not be undesirable

Oligarchy and soft incompleteness

The assumption that the social preference relation is complete is demanding. We distinguish between “hard” and “soft” incompleteness, and explore the social choice implications of the latter. Under soft incompleteness, social preferences can take values in the unit interval. We motivate interest in soft incompleteness by presenting a version of the strong Pareto rule that is suited to the context of a [0, 1]-valued social preference relation. Using a novel approach to the quasi-transitivity of this relation we prove a general oligarchy theorem. Our framework allows us to make a distinction between a “strong” and a “weak” oligarchy, and our theorem identifies when the oligarchy must be strong and when it can be weak. Weak oligarchy need not be undesirable