Fair Assignment of Indivisible Chores to Asymmetric Agents

2025-10-12

AI Summary

This paper studies the fair allocation of indivisible chores among asymmetric agents with distinct weights, aiming to maximize the minimum weighted maximin share (WMMS) guarantee. While prior work only established an $O(log n)$-WMMS existence guarantee for chores, the analogous problem for goods admits an optimal $n$-WMMS bound. We present the first constant-factor approximation: for any $n$ weighted agents, there always exists a feasible allocation achieving $20$-WMMS—i.e., each agent’s disutility is at most 20 times its individual WMMS value. This constant factor breaks the previous logarithmic upper bound and yields the first constant multiplicative approximation guarantee for fair chore allocation under asymmetric weights. Technically, our approach integrates refined WMMS modeling, careful partitioning of resources, and combinatorial pairing arguments, substantially strengthening theoretical guarantees for weighted fair division.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We consider the problem of assigning indivisible chores to agents with different entitlements in the maximin share value (MMS) context. While constant-MMS allocations/assignments are guaranteed to exist for both goods and chores in the symmetric setting, the situation becomes much more complex when agents have different entitlements. For the allocation of indivisible goods, it has been proven that an $n$-WMMS (weighted MMS) guarantee is the best one can hope for. For indivisible chores, however, it was recently discovered that an $O(log n)$-WMMS assignment is guaranteed to exist. In this work, we improve this upper bound to a constant-WMMS guarantee.footnote{We prove the existence of a 20-WMMS assignment, but we did not attempt to optimize the constant factor. We believe our methods already yield a slightly better bound with a tighter analysis.}

Problem

• Fairly assigning indivisible chores to asymmetric agents
• Improving weighted maximin share guarantees for chore allocation
• Establishing constant-factor approximation for asymmetric agents

Innovation

• Achieves constant-factor WMMS guarantee for chores
• Improves previous O(log n) bound to constant factor
• Applies weighted maximin share to asymmetric agents