Correlation of Rankings in Matching Markets

We study the role of correlation in matching markets, where multiple decision makers simultaneously face selection problems from the same pool of candidates. We propose a model in which a candidate’s priority scores across different decision makers exhibit varying levels of correlation dependent on the candidate’s sociodemographic group. Such differential correlation can arise in school choice because of the varying prevalence of selection criteria, in college admissions because of test-optional policies, or because of algorithmic monoculture, that is, when decision makers rely on the same algorithms and data sets to evaluate candidates. We show that higher correlation for one of the groups generally improves the outcome for all groups, leading to higher efficiency. However, students from a given group are more likely to remain unmatched as their own correlation level increases. This implies that it is advantageous to belong to a low-correlation group. Finally, we extend the tie-breaking literature to multiple priority classes and intermediate levels of correlation. Overall, our results point to differential correlation as a previously overlooked systemic source of group inequalities in school, university, and job admissions.

This paper was accepted by Itai Ashlagi, revenue management and market analytics.

Funding: This work was partially supported by MIAI @ Grenoble Alpes [Grants ANR-19-P3IA-0003 and ANR-23-PEIA-0003], by the French National Research Agency (ANR) [Grants ANR-19-CE48-0018 and ANR-20-CE23-0007], and by the National Science Foundation [Grant DMS-1928930] and by the Alfred P. Sloan Foundation [Grant G-2021-16778], which funded B. Pradelski’s residency at the Simons Laufer Mathematical Sciences Institute (formerly MSRI) in Berkeley, CA, during the Fall 2023 semester.

Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.06067.