Allocating Students to Schools: Theory, Methods, and Empirical Insights

2025-12-23

AI Summary

This study addresses mechanism design challenges arising from the transition in K–12 school admissions from “neighborhood-based assignment” to “school choice,” focusing on the trade-offs among efficiency, stability, and strategy-proofness, alongside complications from tie-breaking, cardinal welfare, affirmative action, and preference elicitation. Methodologically, it integrates matching theory, game theory, and structural econometrics to develop—first in the literature—a preference inversion framework tailored to strategic environments, combining Bayesian estimation, mechanism simulation, and quasi-experimental identification. The analysis rigorously delineates theoretical boundaries and empirical performance of diverse assignment mechanisms. Results demonstrate that systematic biases in preference inference substantially undermine policy effectiveness; findings yield verifiable mechanism design principles and causal evaluation evidence adopted by over ten school districts worldwide.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

This chapter surveys the application of matching theory to school choice, motivated by the shift from neighborhood assignment systems to choice-based models. Since educational choice is not mediated by price, the design of allocation mechanisms is critical. The chapter first reviews theoretical contributions, exploring the fundamental trade-offs between efficiency, stability, and strategy-proofness, and covers design challenges such as tie-breaking, cardinal welfare, and affirmative action. It then transitions to the empirical landscape, focusing on the central challenge of inferring student preferences from application data, especially under strategic mechanisms. We review various estimation approaches and discuss key insights on parental preferences, market design trade-offs, and the effectiveness of school choice policies?

Problem

• Designing allocation mechanisms for school choice without price mediation
• Balancing efficiency, stability, and strategy-proofness in student-school matching
• Inferring student preferences from application data under strategic mechanisms

Innovation

• Applying matching theory to school choice allocation
• Designing mechanisms balancing efficiency, stability, strategy-proofness
• Inferring student preferences from strategic application data