Respecting priorities versus respecting preferences in school choice: When is there a trade-off?

TL;DR

This paper investigates the conditions under which the student-proposing deferred acceptance algorithm (DA) is efficient in school choice markets, especially when balancing priorities and preferences, and introduces a new generalized condition.

Contribution

It introduces a new condition that broadens the understanding of when DA is efficient, extending previous results by focusing on relevant parts of preferences and priorities.

Findings

The new condition generalizes earlier efficiency conditions.

DA is efficient in all environments with a unique priority-respecting allocation.

Simulations show the condition significantly expands known efficient environments.

Abstract

A classic trade-off that school districts face when deciding which matching algorithm to use is that it is not possible to always respect both priorities and preferences. The student-proposing deferred acceptance algorithm (DA) respects priorities but can lead to inefficient allocations. We identify a new condition on school choice markets under which DA is efficient. Our condition generalizes earlier conditions by placing restrictions on how preferences and priorities relate to one another only on the parts that are relevant for the assignment. Whenever there is a unique allocation that respects priorities, our condition captures all the environments for which DA is efficient. We show through stylized examples and simulations that our condition significantly expands the range of known environments for which DA is efficient. We also discuss how our condition sheds light on existing empirical findings.