Approximate and Strategyproof Maximin Share Allocation of Chores with Ordinal Preferences

TL;DR

This paper introduces new algorithms for fair allocation of chores based solely on ordinal preferences, achieving improved approximation ratios and considering strategic behavior of agents.

Contribution

It presents a simple deterministic 5/3-approximation algorithm for chore allocation and improved randomized algorithms for strategic settings, surpassing previous results.

Findings

Deterministic 5/3-approximation algorithm for chores

Optimal for n=2,3 agents

Randomized algorithms achieve O(\sqrt{ ext{log} n}) approximation in strategic settings

Abstract

We initiate the work on maximin share (MMS) fair allocation of m indivisible chores to n agents using only their ordinal preferences, from both algorithmic and mechanism design perspectives. The previous best-known approximation is 2-1/n by Aziz et al. [IJCAI 2017]. We improve this result by giving a simple deterministic 5/3-approximation algorithm that determines an allocation sequence of agents, according to which items are allocated one by one. By a tighter analysis, we show that for n=2,3, our algorithm achieves better approximation ratios, and is actually optimal. We also consider the setting with strategic agents, where agents may misreport their preferences to manipulate the outcome. We first provide a O(\log (m/n))-approximation consecutive picking algorithm, and then improve the approximation ratio to O(\sqrt{\log n}) by a randomized algorithm. Our results uncover some interesting contrasts between the approximation ratios achieved for chores versus goods.