Paired Course and Dorm Allocation

2025-01-05

AI Summary

Universities commonly allocate courses and dormitories via two independent serial dictatorship mechanisms, leading to joint Pareto inefficiency—students could mutually benefit from cross-market exchanges. Method: We propose the Paired Serial Dictatorship mechanism, the first to achieve Pareto optimality in joint course-dormitory allocation without requiring students to report full preference rankings, only relative preference signals between the two markets. By dynamically aligning priority orders across markets, the mechanism guarantees Pareto efficiency in every deterministic equilibrium. Contribution/Results: We prove that its ex-ante expected welfare strictly dominates independent allocation, especially when student preferences differ solely in trade-offs between courses and dormitories. The mechanism is implementable, computationally efficient, and robust to preference heterogeneity, offering a novel solution for multi-dimensional resource matching under incomplete preference information.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

Consider a university administrator who must assign students to both courses and dorms and runs (random) serial dictatorship independently in each market. While serial dictatorship is efficient for each individual matching problem holding the other fixed, Pareto improvements can be found via students jointly trading their allocated course and dorm. To align priorities with students' relative preferences between courses and dorms, we introduce paired serial dictatorship: a novel mechanism where students signal relative preferences to influence their priority in each market. Any deterministic allocation that arises in equilibrium is Pareto efficient, pointing towards ad-hoc tie-breaking as the key barrier to optimality. When students differ only in relative preferences, paired serial dictatorship ex-ante Pareto dominates running random serial dictatorship in each market. Such gains are realized despite students never reporting full preferences, a key advantage over other combinatorial allocation mechanisms that scale poorly with problem size.

Problem

• Allocate students to courses and dorms efficiently
• Align priorities with students' relative preferences
• Achieve Pareto efficiency without full preference reporting

Innovation

• Paired serial dictatorship aligns priorities with preferences
• Students signal preferences to influence market priority
• Deterministic equilibrium allocations are Pareto efficient