Social Welfare in Budget Aggregation

2026-02-26

AI Summary

This study addresses the fundamental challenge in budget aggregation of simultaneously achieving proportional fairness, maximizing social welfare, and ensuring strategyproofness. Focusing on the ℓ₁ utility model, the work proposes UtilProp—the first truthful proportional mechanism that attains the optimal worst-case social welfare ratio under single-peaked preferences—and introduces the notion of “decomposability” to design GreedyDecomp, an approximately optimal mechanism. Theoretical analysis shows that UtilProp dominates all known single-peaked, proportional, and truthful mechanisms in terms of social welfare, while GreedyDecomp achieves a 2-approximation of UtilDecomp’s welfare and preserves the optimal worst-case welfare ratio, all while maintaining decomposability. By integrating mechanism design, worst-case analysis, and approximation algorithms, this research systematically characterizes the trade-offs among these three desiderata.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Security and Privacy: Large-scale security measurements

Abstract

We study budget aggregation under $\ell_1$-utilities, a model for collective decision making in which agents with heterogeneous preferences must allocate a public budget across a set of alternatives. Each agent reports their preferred allocation, and a mechanism selects an allocation. Early work focused on social welfare maximization, which in this setting admits truthful mechanisms, but may underrepresent minority groups, motivating the study of proportional mechanisms. However, the dominant proportionality notion, single-minded proportionality, is weak, as it only constrains outcomes when agents hold extreme preferences. To better understand proportionality and its interaction with welfare and truthfulness, we address three questions. First, how much welfare must be sacrificed to achieve proportionality? We formalize this via the price of proportionality, the best worst-case welfare ratio between a proportional mechanism and Util, the welfare-maximizing mechanism. We introduce a new single-minded proportional and truthful mechanism, UtilProp, and show that it achieves the optimal worst-case ratio. Second, how do proportional mechanisms compare in terms of welfare? We define an instance-wise welfare dominance relation and use it to compare mechanisms from the literature. In particular, we show that UtilProp welfare-dominates all previously known single-minded proportional and truthful mechanisms. Third, can stronger notions of proportionality be achieved without compromising welfare guarantees? We answer this question in the affirmative by studying decomposability and proposing GreedyDecomp, a decomposable mechanism with optimal worst-case welfare ratio. We further show that computing the welfare-dominant decomposable mechanism, UtilDecomp, is NP-hard, and that GreedyDecomp provides a 2-approximation to UtilDecomp in terms of welfare.

Problem

• budget aggregation
• social welfare
• proportionality
• truthfulness
• fairness

Innovation

• budget aggregation
• proportionality
• social welfare
• truthful mechanism
• decomposability