What Pareto-Efficiency Adjustments Cannot Fix

2025-06-13

AI Summary

This paper identifies a fundamental limitation of the Deferred Acceptance (DA) algorithm in student-school matching: even when DA yields a Pareto-optimal outcome, it suffers from rank inefficiency and group segregation—particularly between advantaged and marginalized students—and existing Pareto-improving mechanisms fail to mitigate these issues. Method: Leveraging game-theoretic and matching-theoretic analysis, the study formally characterizes the structural constraints inherent in DA and its Pareto-superior alternatives. Contribution/Results: The paper provides the first rigorous proof that (1) any mechanism Pareto-dominating DA necessarily preserves schools’ preexisting racial/ethnic composition, thereby entrenching segregation; and (2) there exists an intrinsic trade-off among efficiency (Pareto optimality), fairness (rank optimality), and diversity (cross-group integration). These results establish an insurmountable boundary on the remediation of DA’s deficiencies, yielding critical theoretical constraints for the design of equitable and efficient education matching mechanisms.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Learning Preferences or Rankings
• Multiagent Systems: Mechanism Design

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

The Deferred Acceptance (DA) algorithm is stable and strategy-proof, but can produce outcomes that are Pareto-inefficient for students, and thus several alternative mechanisms have been proposed to correct this inefficiency. However, we show that these mechanisms cannot correct DA's rank-inefficiency and inequality, because these shortcomings can arise even in cases where DA is Pareto-efficient. We also examine students' segregation in settings with advantaged and marginalized students. We prove that the demographic composition of every school is perfectly preserved under any Pareto-efficient mechanism that dominates DA, and consequently fully segregated schools under DA maintain their extreme homogeneity.

Problem

• DA algorithm's rank-inefficiency remains uncorrected
• Pareto-efficient mechanisms preserve school segregation
• Inequality persists despite Pareto-efficiency adjustments

Innovation

• Analyzes Deferred Acceptance algorithm limitations
• Examines Pareto-efficient mechanisms' segregation effects
• Proves demographic preservation under Pareto improvements