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

TL;DR

The paper identifies and corrects a minor bug in Erdil & Ergin's (2008) replication code for stable improvement cycles in school-choice matchings. It presents a concrete counterexample to illustrate the bug's effect and provides a corrected implementation (with a detailed update rule) and GitHub link. Re-analysis shows the corrected code yields fewer improving students but larger average rank improvements, while the core theoretical results remain valid. The work enhances replication integrity and informs interpretation of computational findings in the school-choice literature.

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.

Figures (3)

• Figure 1: Percent of improving students as a function of $\alpha$ (1,000 students and 20 schools).
• Figure 2: Average improvement in rank among improving students as a function of $\alpha$ (1,000 students and 20 schools).
• Figure 3: Relative improvement in average rank of the matchings returned by corrected code, in comparison to the original code, as a function of $\alpha$.