With a Preference for Priority: Explaining Variations of Stability and Efficiency in School Choice

Abstract: In school choice systems, policy makers try to allocate students in a fair and efficient way. Two mechanisms for allocating students that has been of particular interest for market designers is Deferred Acceptance (DA), which is stable and does not allow for priority violations, and Top Trading Cycles (TTC), which is Pareto efficient but creates justified envy among students. Here, we propose that the degrees of inefficiency in DA and justified envy in TTC is affected by how well students' preferences over schools correlates with schools' priorities over students. We simulate random school markets under varying assumptions of students' utility functions to derive this relationship. Additionally, by using data from school choice to elementary schools in the Swedish municipality Järfälla, we explore how the preference-priority correlation affects allocations there, and approximate the actual correlation in the area. We find that DA is closer to being efficient and TTC is closer to being stable for higher levels of preference-priority correlations. We also find that the relative desirability of the two mechanism differ in a systematic fashion, depending on the institutional setting. Specifically, DA is a relatively more desirable than TTC for higher correlations compared to lower correlations. When correlation decreases, Pareto improving trades become less costly in terms of blocking pairs for a DA to TTC switch -- and the choice for policy makers less straightforward. Finally, we discuss the relevance of our results in light of an increased attention from policy makers to segregation and equity in school choice.