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Matching with Committee Preferences

Haoyu Song, Thanh Nguyen, Young-san Lin

Abstract

We study a many-to-one matching model inspired by school choice, where schools evaluate applicants using multiple rankings rather than a single priority order. We model each school's evaluation with social choice criteria to reflect the school's internal ranking process. In particular, we define acceptable choices as candidates ranked above a top percentile of the accepted cohort by a sufficient number of evaluators. Stability is then defined in terms of acceptability: accepted candidates must receive strong support, while rejected candidates receive at most weak support. Since exact acceptability and stability may not exist, we construct approximately stable outcomes using a new equilibrium concept that combines matching with a Lindahl equilibrium over ordinal preferences, providing a flexible, equilibrium-based framework for committee-based matching markets.

Matching with Committee Preferences

Abstract

We study a many-to-one matching model inspired by school choice, where schools evaluate applicants using multiple rankings rather than a single priority order. We model each school's evaluation with social choice criteria to reflect the school's internal ranking process. In particular, we define acceptable choices as candidates ranked above a top percentile of the accepted cohort by a sufficient number of evaluators. Stability is then defined in terms of acceptability: accepted candidates must receive strong support, while rejected candidates receive at most weak support. Since exact acceptability and stability may not exist, we construct approximately stable outcomes using a new equilibrium concept that combines matching with a Lindahl equilibrium over ordinal preferences, providing a flexible, equilibrium-based framework for committee-based matching markets.
Paper Structure (21 sections, 61 equations, 1 figure)

This paper contains 21 sections, 61 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Model
  3. Acceptable Choice Set
  4. Stable Matching
  5. Approximate Acceptable Choice Set
  6. Multiple Schools: A Matching Problem
  7. MEO: Matching Equilibrium with Ordinal Preferences
  8. Stable Fractional Matchings from MEO
  9. Rounding
  10. Conclusion
  11. Rounding Lemmas
  12. Proof of Lemma \ref{['lemma:round']}
  13. Proof of Lemma \ref{['lemma:iterround']}
  14. Equilibrium Existence
  15. Proof of Theorem \ref{['thm:LEO_existence']}
  16. ...and 6 more sections

Figures (1)

  • Figure 1: $\alpha_k$-ranked student

Theorems & Definitions (16)

  • proof
  • proof
  • proof
  • proof
  • proof : Proof of Theorem \ref{['thm:LEO_existence']}
  • proof : Proof of Theorem \ref{['thm:meo_existence']}
  • proof
  • proof
  • proof
  • proof
  • ...and 6 more