Efficient and Envy-free Random Assignment Beyond Expected Utility

2026-06-11

AI Summary

This study addresses the challenge of achieving efficient and envy-free random allocations when agents’ preferences violate classical assumptions such as independence or transitivity. By extending the Hylland–Zeckhauser pseudomarket mechanism, the paper constructs weakly efficient and envy-free assignments within a general framework of abstract, continuous, convex preferences. Specifically, for non-transitive and non-independent preferences represented by skew-symmetric bilinear (SSB) utility functions, the authors establish the existence of allocations that are both efficient and approximately envy-free. This work transcends the limitations of expected utility theory by simultaneously guaranteeing efficiency and fairness under generalized preference structures—a first in the literature—and further demonstrates that existing ordinal mechanisms, such as probabilistic serial rules, fail to achieve either efficiency or fairness in this broader setting.

Abstract

We consider the random assignment problem with abstract continuous and convex preferences. In particular, we admit preference relations that are not constrained by independence or transitivity. By extending the Hylland--Zeckhauser pseudo-market mechanism, we show that weakly efficient and envy-free random assignments always exist. For preferences that can be represented via skew-symmetric bilinear (SSB) utility functions -- which generalize linear expected utility functions -- we prove the existence of efficient and approximately envy-free random assignments. Efficient and envy-free random assignments exist under a mild additional assumption on preferences. These findings have notable implications for ordinal random assignment, where ordinal preferences are extended to preferences over lotteries via the pairwise comparison (PC) extension. While the probabilistic serial rule and popular random assignments frequently and significantly violate PC-efficiency and PC-envy-freeness, respectively, random assignments that satisfy both conditions do exist.

Problem

• random assignment
• envy-freeness
• efficiency
• non-expected utility
• ordinal preferences

Innovation

• random assignment
• envy-freeness
• efficiency
• SSB utility
• pseudo-market mechanism