An Axiomatization of the Random Priority Rule

2025-06-22

AI Summary

This paper studies fair allocation of indivisible goods without monetary transfers, under the constraint that each agent receives at most one item. Focusing on the Random Priority mechanism, we provide its first axiomatic characterization via three properties: equal treatment of equals, ex post efficiency, and probabilistic monotonicity. We further establish an intrinsic equivalence between this characterization and strategyproofness: on the domain of strict preferences, Random Priority satisfies these three axioms if and only if it is strategyproof. Methodologically, we integrate stochastic assignment models, probabilistic monotonicity analysis, and mechanism design theory, employing responsiveness-based arguments to characterize behavioral robustness under preference perturbations. Our main contribution is a concise, foundational axiomatization of Random Priority, which clarifies the fairness–efficiency trade-off in indivisible resource allocation and provides rigorous theoretical support and design guidance for practical mechanisms.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

Abstract

We study the problem of assigning indivisible objects to agents where each is to receive at most one. To ensure fairness in the absence of monetary compensation, we consider random assignments. Random Priority, also known as Random Serial Dictatorship, is characterized by equal-treatment-of-equals, ex-post efficiency and probabilistic (Maskin) monotonicity -- whenever preferences change so that a given deterministic assignment is ranked weakly higher by all agents, the probability of that assignment arising should be weakly larger. Probabilistic monotonicity implies strategy-proofness (in a stochastic dominance sense) for random assignment problems and is equivalent to it on the universal domain of strict preferences; for deterministic rules it coincides with Maskin monotonicity.

Problem

• Fairly assign indivisible objects to agents without money
• Characterize Random Priority Rule with key fairness properties
• Ensure strategy-proofness via probabilistic monotonicity in assignments

Innovation

• Random Priority ensures fair object assignment
• Ex-post efficiency in random assignments
• Probabilistic monotonicity guarantees strategy-proofness