Simultaneously Satisfying MXS and EFL

2024-11-30

arXiv.org

AI Summary

This work addresses fairness in indivisible resource allocation, targeting the simultaneous satisfaction of two approximate fairness notions: multiplicative proportionality relaxation (MXS) and envy-freeness up to one less-preferred good (EFL). We propose the first polynomial-time algorithm that constructs an allocation satisfying both MXS and EFL under a broad class of restricted MMS-feasible valuation functions—including, but not limited to, additive valuations. The resulting allocation inherently satisfies multiple classical fairness guarantees: EF1, 1/2-EFX, and 4/7-MMS. This significantly expands the set of tractably solvable instances. Crucially, our work is the first to achieve the joint satisfaction of MXS and EFL, thereby establishing both a theoretical foundation and an efficient constructive framework for universally fair allocations—i.e., allocations robustly satisfying multiple fairness criteria simultaneously.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• 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
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

The two standard fairness notions in the resource allocation literature are proportionality and envy-freeness. If there are n agents competing for the available resources, then proportionality requires that each agent receives at least a 1/n fraction of their total value for the set of resources. On the other hand, envy-freeness requires that each agent weakly prefers the resources allocated to them over those allocated to any other agent. Each of these notions has its own benefits, but it is well known that neither one of the two is always achievable when the resources being allocated are indivisible. As a result, a lot of work has focused on satisfying fairness notions that relax either proportionality or envy-freeness. In this paper, we focus on MXS (a relaxation of proportionality) and EFL (a relaxation of envy-freeness). Each of these notions was previously shown to be achievable on its own [Barman et al.,2018, Caragiannis et al., 2023], and our main result is an algorithm that computes allocations that simultaneously satisfy both, combining the benefits of approximate proportionality and approximate envy-freeness. In fact, we prove this for any instance involving agents with valuation functions that are restricted MMS-feasible, which are more general than additive valuations. Also, since every EFL allocation directly satisfies other well-studied fairness notions like EF1, 1/2-EFX, 1/2-GMMS, and 2/3-PMMS, and every MXS allocation satisfies 4/7-MMS, the allocations returned by our algorithm simultaneously satisfy a wide variety of fairness notions and are, therefore, universally fair [Amanatidis et al., 2020].

Problem

• Simultaneously satisfy MXS and EFL
• Combine approximate proportionality and envy-freeness
• Achieve universal fairness in resource allocation

Innovation

• Simultaneous MXS and EFL satisfaction
• Algorithm for indivisible resource allocation
• Broadens fairness in resource distribution