How to Balance Preferences and Predicted Outcomes in Refugee and School Assignments

🔧 A New Constrained Priority Mechanism

A constrained priority mechanism is introduced that blends outcome-based matching (from machine learning predictions) with traditional preference-based allocation. The design lets a planner enforce a minimum average outcome while still assigning agents according to their ranked preferences.

🧾 Real-world Applications and Data

• Illustrations use real-world data on two assignment problems: refugee families to host-country locations and kindergarteners to schools.
• In these applications, the outcome score is interpreted as:
• the predicted probability of employment for refugee families, and
• standardized test scores for students.

📈 How the Mechanism Operates

• The planner specifies a minimum acceptable average outcome threshold ḡ (denoted \bar g).
• The mechanism is a priority-based assignment rule that considers agents in priority order and assigns them according to their preferences, but only so long as the final matching meets the planner’s specified threshold ḡ.
• Outcome predictions come from machine-learning models and are incorporated into the feasibility constraint for the assignment.

📌 Key Theoretical Properties

• Strategy-proof: no agent can benefit by misrepresenting preferences under the mechanism.
• Constrained efficient: the mechanism always produces a matching that is not Pareto dominated by any other matching that also satisfies the planner’s threshold ḡ.

⚖️ Why This Matters

This approach provides a practical way for planners to enforce minimum welfare or performance standards—expressed through predictive outcome scores—while preserving agents’ preference-based assignments and important incentive and efficiency guarantees. The mechanism therefore offers a transparent tool for policy settings where predicted outcomes and individual preferences both matter.