Proportional and Pareto-Optimal Allocation of Chores with Subsidy

Jugal Garg, Eklavya Sharma, Xiaowei Wu

Keywords: fair division, fair allocation, subsidy, proportionality, po, pareto optimality

TL;DR: For the problem of fairly and efficiently allocating chores among $n$ agents with different weights, we show that a proportional and Pareto-optimal allocation can be computed with a subsidy of at most $n/3$ using a very simple algorithm.

Abstract:

We consider the problem of allocating $m$ indivisible chores among $n$ agents with possibly different weights, aiming for a solution that is both fair and efficient. Specifically, we focus on the classic fairness notion of proportionality and efficiency notion of Pareto-optimality. Since proportional allocations may not always exist in this setting, we allow the use of subsidies (monetary compensation to agents) to ensure agents are proportionally-satisfied, and aim to minimize the total subsidy required. Wu and Zhou (WINE 2024) showed that when each chore has disutility at most 1, a total subsidy of at most $n/3 - 1/6$ is sufficient to guarantee proportionality. However, their approach is based on a complex technique, which does not guarantee economic efficiency — a key desideratum in fair division.

In this work, we give a polynomial-time algorithm that achieves the same subsidy bound while also ensuring Pareto-optimality. Moreover, both our algorithm and its analysis are significantly simpler than those of Wu and Zhou (WINE 2024). Our approach first computes a proportionally-fair competitive equilibrium, and then applies a rounding procedure guided by minimum-pain-per-buck edges.

Area: Game Theory and Economic Paradigms (GTEP)

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Submission Number: 1208