Maximum Welfare Allocations under Quantile Valuations

2025-02-25

AI Summary

This paper studies the allocation of indivisible goods under quantile-based valuations, aiming to maximize two welfare objectives: utilitarian (sum) welfare and egalitarian (minimum quantile) welfare. Departing from standard additive utility assumptions, the authors introduce the quantile valuation model—where each agent’s utility for a bundle equals a specified quantile of the individual values of items in that bundle—to capture heterogeneous preference structures. Theoretically, the work identifies allocation balance as a critical determinant of computational complexity. Algorithmically, it provides a polynomial-time algorithm with optimal approximation ratio for utilitarian welfare, and an exact polynomial-time algorithm for egalitarian welfare under a key tractable case. Collectively, these contributions significantly advance the joint optimization of efficiency and fairness in indivisible goods allocation.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We propose a new model for aggregating preferences over a set of indivisible items based on a quantile value. In this model, each agent is endowed with a specific quantile, and the value of a given bundle is defined by the corresponding quantile of the individual values of the items within it. Our model captures the diverse ways in which agents may perceive a bundle, even when they agree on the values of individual items. It enables richer behavioral modeling that cannot be easily captured by additive valuation functions. We study the problem of maximizing utilitarian and egalitarian welfare within the quantile-based valuation setting. For each of the welfare functions, we analyze the complexity of the objectives. Interestingly, our results show that the complexity of both objectives varies significantly depending on whether the allocation is required to be balanced. We provide near-optimal approximation algorithms for utilitarian welfare, and for egalitarian welfare, we present exact algorithms whenever possible.

Problem

• Maximizing welfare under quantile-based valuations
• Analyzing complexity of utilitarian and egalitarian objectives
• Developing approximation and exact algorithms for welfare optimization

Innovation

• Quantile-based valuation model
• Utilitarian welfare algorithms
• Egalitarian welfare exact algorithms