Equitable Allocations of Indivisible Goods

TL;DR

This paper explores fair division of indivisible goods, demonstrating algorithms that achieve equitability, Pareto optimality, and their combinations, supported by experiments on real data.

Contribution

It introduces a novel algorithm guaranteeing Pareto optimality and equitability up to one good, advancing fair division methods for indivisible items.

Findings

Leximin algorithm satisfies equitability up to any good and Pareto optimality.

New algorithm guarantees Pareto optimality and equitability up to one good in pseudopolynomial time.

Experiments show multiple fairness and efficiency criteria can be achieved simultaneously.

Abstract

In fair division, equitability dictates that each participant receives the same level of utility. In this work, we study equitable allocations of indivisible goods among agents with additive valuations. While prior work has studied (approximate) equitability in isolation, we consider equitability in conjunction with other well-studied notions of fairness and economic efficiency. We show that the Leximin algorithm produces an allocation that satisfies equitability up to any good and Pareto optimality. We also give a novel algorithm that guarantees Pareto optimality and equitability up to one good in pseudopolynomial time. Our experiments on real-world preference data reveal that approximate envy-freeness, approximate equitability, and Pareto optimality can often be achieved simultaneously.