Matching with Committee Preferences

TL;DR

This paper introduces a new model for many-to-one matching inspired by school choice, where schools evaluate applicants with multiple rankings, and proposes an equilibrium-based framework for approximate stability.

Contribution

It develops a novel approach combining social choice criteria with matching theory to handle multi-ranking evaluations and introduces an equilibrium concept for approximate stability.

Findings

Defined acceptability based on top percentile rankings supported by multiple evaluators

Constructed approximately stable outcomes using a Lindahl equilibrium framework

Provided a flexible, equilibrium-based approach for committee-based matching markets

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.