Reducing Leximin Fairness to Utilitarian Optimization

2024-09-16

AAAI Conference on Artificial Intelligence

AI Summary

This paper addresses the computational intractability of Leximin fairness optimization—i.e., lexicographically maximizing the sorted vector of utilities (smallest, second-smallest, etc.). We propose the first robust reduction framework that transforms Leximin fairness into tractable utilitarian optimization (i.e., sum-utility maximization). Our method leverages probabilistic distribution construction and ordinal fairness modeling, employing randomized reduction to map deterministic Leximin solutions to randomized solutions satisfying the *expected Leximin order*. The framework is solver-agnostic: it integrates seamlessly with standard utilitarian solvers (e.g., LP/IP) and preserves approximation guarantees—any α-approximate utilitarian solver yields an α-approximate expected-Leximin solution. We validate the approach on social choice tasks including stochastic item allocation, public-good lotteries, and participatory budgeting. Empirically, the generated solutions strictly satisfy the expected Leximin ordering, and theoretical analysis provides rigorous approximation bounds.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Reducing leximin fairness to utilitarian optimization problems
• Producing leximin-fair distributions using utilitarian solvers
• Applying reduction scheme to indivisible goods and participatory budgeting

Innovation

• Reduces leximin fairness to utilitarian optimization problems
• Produces leximin-fair distributions using utilitarian solvers
• Maintains approximation guarantees when using approximate solvers