# Combining Outcome-Based and Preference-Based Matching: A Constrained Priority Mechanism

## TL;DR

This paper presents a new constrained priority mechanism that integrates outcome-based and preference-based matching, ensuring minimum outcome thresholds while respecting preferences, demonstrated through refugee and school assignment applications.

## Contribution

It introduces a novel mechanism combining outcome thresholds with priority-based matching, ensuring strategy-proofness and efficiency in complex allocation problems.

## Key findings

- Mechanism is strategy-proof and constrained efficient.
- Applicable to refugee and school assignment scenarios.
- Ensures minimum outcome thresholds are met.

## Abstract

We introduce a constrained priority mechanism that combines outcome-based matching from machine-learning with preference-based allocation schemes common in market design. Using real-world data, we illustrate how our mechanism could be applied to the assignment of refugee families to host country locations, and kindergarteners to schools. Our mechanism allows a planner to first specify a threshold $\bar g$ for the minimum acceptable average outcome score that should be achieved by the assignment. In the refugee matching context, this score corresponds to the predicted probability of employment, while in the student assignment context it corresponds to standardized test scores. The mechanism is a priority mechanism that considers both outcomes and preferences by assigning agents (refugee families, students) based on their preferences, but subject to meeting the planner's specified threshold. The mechanism is both strategy-proof and constrained efficient in that it always generates a matching that is not Pareto dominated by any other matching that respects the planner's threshold.