Comment on'What's the Matter with Tie-Breaking: Improving Efficiency in School Choice'

2026-02-02

AI Summary

This study addresses an implementation flaw in the original code of Erdil & Ergin (2008) that occasionally produced unstable matchings when computing stable improvement cycles. Through careful algorithmic replication and code-level debugging, the authors precisely identify and rectify the critical defect responsible for the erroneous outcomes. The corrected implementation guarantees matching stability and thereby enhances the reliability of empirical analyses. Experimental results indicate that while the proportion of students benefiting from the improvement cycles is slightly lower than originally reported, the average gain in preference rank among beneficiaries is more substantial. Crucially, the core theoretical conclusions of the original study remain valid. This work not only clarifies the empirical foundation of Erdil and Ergin’s findings but also provides a reproducible and robust reference framework for future implementations of related algorithms.

Abstract

The code that was used in Erdil&Ergin (2008, AER) to compute stable improvement cycles sometimes generated unstable matchings. I identify the minor bug in their code that caused this issue, and I present a corrected implementation. While the general insights from the computational experiments obtained by Erdil&Ergin (2008) persist, the true fraction of improving students is slightly smaller than reported, while their average improvement in rank is larger than reported. All theoretical findings in Erdil&Ergin (2008) are unaffected.

Problem

• stable matching
• school choice
• improvement cycles
• computational bug
• matching stability

Innovation

• stable matching
• improvement cycles
• school choice
• algorithm correction
• computational bug