The cost of strategy-proofness in school choice

TL;DR

This paper compares the outcomes of three school choice algorithms—Deferred Acceptance, Top Trading Cycles, and Rank-Minimizing—to evaluate their efficiency, fairness, and envy, revealing surprising improvements of RM over the others.

Contribution

It introduces the rank-minimizing mechanism as an alternative to traditional algorithms, demonstrating its superior rank efficiency and fairness in school choice settings.

Findings

Rank-minimizing mechanism significantly improves rank efficiency.

RM also enhances placement for the worst-off student.

RM generates less justified envy than TTC.

Abstract

We compare the outcomes of the most prominent strategy-proof and stable algorithm (Deferred Acceptance, DA) and the most prominent strategy-proof and Pareto optimal algorithm (Top Trading Cycles, TTC) to the allocation generated by the rank-minimizing mechanism (RM). While one would expect that RM improves upon both DA and TTC in terms of rank efficiency, the size of the improvement is nonetheless surprising. Moreover, while it is not explicitly designed to do so, RM also significantly improves the placement of the worst-off student. Furthermore, RM generates less justified envy than TTC. We corroborate our findings using data on school admissions in Budapest.