Correlation of Rankings in Matching Markets

2025-12-04

AI Summary

This paper investigates how systematic disparities in inter-decision-maker correlation of preference scores across sociodemographic groups exacerbate inequality in matching markets. Method: We develop a group-differentiated correlation model grounded in game theory, two-sided matching theory, and probabilistic analysis to characterize how varying score correlations affect matching outcomes. Contribution/Results: Contrary to intuition, groups exhibiting lower inter-decision-maker score correlation enjoy higher admission probabilities under multi-decision-maker matching; conversely, high correlation—while improving aggregate matching efficiency—substantially increases intra-group rejection risk. This work identifies differential score correlation as a novel structural driver of group-level inequality in educational and labor-market selection, extending priority-breaking theory. It further demonstrates that algorithmic standardization and score homogenization may inadvertently reinforce systemic inequity.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

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.

Problem

• Examines correlation's impact on fairness in matching markets.
• Analyzes how group-specific correlation affects matching outcomes.
• Identifies correlation as a source of systemic group inequalities.

Innovation

• Model with varying correlation levels across sociodemographic groups
• Extend tie-breaking to multiple priority classes and intermediate correlation
• Show differential correlation as systemic source of group inequalities