Majoritarian Assignment Rules

2026-02-16

AI Summary

This study addresses the problem of fair item allocation in multi-agent systems that simultaneously satisfies majority rule and allocative efficiency. By introducing classical majority-based social choice functions into allocation settings, the work establishes an almost one-to-one correspondence between preference profiles and majority graphs through the structural properties of the allocation domain, enabling analysis of allocation characteristics via majority graphs. The central contribution is a complete characterization of the possible structures of top cycles, proving that every Pareto-optimal allocation must be semi-popular and lie within a top cycle. Furthermore, the study reveals that top cycles can only contain 1, 2, n−2, n−1, or all n allocations, while the uncovered set remains extremely small—providing a solid theoretical foundation for efficiently searching high-quality allocations.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Fair Division
• Knowledge Representation and Reasoning: Preferences

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

A central problem in multiagent systems is the fair assignment of objects to agents. In this paper, we initiate the analysis of classic majoritarian social choice functions in assignment. Exploiting the special structure of the assignment domain, we show a number of surprising results with no counterparts in general social choice. In particular, we establish a near one-to-one correspondence between preference profiles and majority graphs. This correspondence implies that key properties of assignments -- such as Pareto-optimality, least unpopularity, and mixed popularity -- can be determined solely by the associated majority graph. We further show that all Pareto-optimal assignments are semi-popular and belong to the top cycle. Elements of the top cycle can thus easily be found via serial dictatorships. Our main result is a complete characterization of the top cycle, which implies the top cycle can only consist of one, two, all but two, all but one, or all assignments. By contrast, we find that the uncovered set contains only very few assignments.

Problem

• majoritarian assignment
• fair allocation
• multiagent systems
• social choice
• majority graph

Innovation

• majority graph
• top cycle
• Pareto-optimality
• assignment rules
• social choice