Reducing Leximin Fairness to Utilitarian Optimization

TL;DR

This paper introduces a reduction method that transforms utilitarian optimization algorithms into solutions that approximate leximin fairness in expectation, applicable to various social choice problems.

Contribution

It provides a robust reduction scheme from utilitarian to leximin fairness, preserving approximation guarantees across different social choice settings.

Findings

The scheme converts utilitarian solutions into approximately leximin fair lotteries.

It is robust to approximate utilitarian solvers, maintaining fairness guarantees.

Applicable to stochastic allocations, giveaway lotteries, and participatory budgeting.

Abstract

Two prominent objectives in social choice are utilitarian - maximizing the sum of agents' utilities, and leximin - maximizing the smallest agent's utility, then the second-smallest, etc. Utilitarianism is typically computationally easier to attain but is generally viewed as less fair. This paper presents a general reduction scheme that, given a utilitarian solver, produces a distribution over states (deterministic outcomes) that is leximin in expectation. Importantly, the scheme is robust in the sense that, given an approximate utilitarian solver, it produces a lottery that is approximately-leximin (in expectation) - with the same approximation factor. We apply our scheme to several social choice problems: stochastic allocations of indivisible goods, giveaway lotteries, and fair lotteries for participatory budgeting.