Allocating Chores with Restricted Additive Costs: Achieving EFX, MMS, and Efficiency Simultaneously

2026-03-17

AI Summary

This work addresses the problem of chore allocation under a restricted additive cost model—such as assigning paper reviewing tasks—where each item incurs either zero or a fixed cost to an agent. The authors propose a polynomial-time algorithm that simultaneously achieves two strong fairness guarantees, EFX (envy-freeness up to any good) and MMS (maximin share), while attaining a 2-approximation to the optimal social cost. They further establish that this 2-approximation ratio is theoretically tight. When relaxing the fairness requirements slightly, the algorithm yields weaker yet more tractable fairness guarantees, still computable in polynomial time. By bridging combinatorial optimization with fair division theory, this study introduces a novel paradigm for achieving both efficiency and fairness in resource allocation under constrained cost structures.

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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In a web-based review platform, papers from various research fields must be assigned to a group of reviewers. Each paper has an inherent cost, which represents the effort required for reading and evaluating it (e.g., the paper's length). Reviewers can bid on papers they are interested in, and if they are assigned a paper they have bid on, no cost is incurred. Otherwise, the inherent cost $c(e)$ for paper $e$ applies. We capture this with a model of restricted additive costs: every item $e$ has a cost $c(e)$, and each agent either incurs $0$ or $c(e)$ for $e$. In this work, we study how to allocate such chores fairly and efficiently. We propose an algorithm for computing allocations that are both EFX and MMS. Furthermore, we show that our algorithm achieves a $2$-approximation of the optimal social cost, and the approximation ratio is optimal. We also show that slightly weaker fairness guarantees can be obtained if one requires the algorithm to run in polynomial time.

Problem

• fair division
• chores allocation
• restricted additive costs
• EFX
• MMS

Innovation

• EFX
• MMS
• restricted additive costs
• fair allocation
• approximation algorithm