Correlation of Rankings in Matching Markets

TL;DR

This paper examines how correlation in candidate rankings across decision-makers affects matching market outcomes, revealing that higher correlation improves efficiency but can increase unmatched students within certain groups, highlighting systemic inequalities.

Contribution

It introduces a model linking correlation levels to group-specific outcomes in matching markets, extending tie-breaking analysis to multiple classes and correlation levels.

Findings

Higher correlation improves overall efficiency.

Increased correlation raises unmatched students within a group.

Low-correlation groups have advantages in matching outcomes.

Abstract

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 due to the varying prevalence of selection criteria, in college admissions due to test-optional policies, or due to 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.