Utilitarian Guarantees for the Method of Equal Shares

2025-11-25

AI Summary

This paper addresses the utility loss incurred by the Method of Equal Shares (MES) in participatory budgeting (PB), which ensures fairness—e.g., extended justified representation (EJR)—but may sacrifice aggregate welfare. For DNS-class satisfaction functions, we establish the first provable lower bound on MES’s minimum total utility and conduct a parameterized analysis of how project cost heterogeneity—particularly the ratio of minimum to maximum cost—affects utility guarantees. We prove that this bound is asymptotically tight under the constraint of single-project EJR; when all projects have equal costs, it recovers the known tight bound for multiwinner elections. Our work unifies and improves utilitarian guarantees under two dominant utility measures, providing the first cost-sensitive theoretical characterization of the fairness–efficiency trade-off in PB.

Technology Category

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

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
• Security and Privacy: Large-scale security measurements

Abstract

In recent years, research in Participatory Budgeting (PB) has put a greater emphasis on rules satisfying notions of fairness and proportionality, with the Method of Equal Shares (MES) being a prominent example. However, proportionality can come at a cost to the total utilitarian welfare. Our work formalizes this relationship, by deriving minimum utilitarian welfare guarantees for MES for a subclass of satisfaction functions called DNS functions, which includes two of the most popular ways of measuring a voter's utility in the PB setting: considering (1) the total cost of approved projects or (2) the total number of those projects. Our results are parameterized in terms of minimum and maximum project costs, which allows us to improve on the mostly negative results found in prior studies, and reduce to the existing multiwinner guarantee when project costs are equal. We show that our guarantees are asymptotically tight for rules satisfying Extended Justified Representation up to one project, showing that no proportional rule can achieve a better utilitarian guarantee than MES.

Problem

• Analyzes utilitarian welfare guarantees for Method of Equal Shares in Participatory Budgeting
• Derives minimum welfare bounds for DNS utility functions with varying project costs
• Shows guarantees are asymptotically tight for proportional voting rules

Innovation

• Derives utilitarian welfare guarantees for MES
• Parameterizes results using project cost ranges
• Shows guarantees are asymptotically tight