Method of Equal Shares with Bounded Overspending

2024-09-23

arXiv.org

AI Summary

This paper addresses the longstanding tension between proportionality and efficiency in participatory budgeting (PB). We propose Bounded Overspending Equal Shares (BOS-ES), the first Equal Shares variant incorporating bounded overspending—thereby relaxing strict proportionality while preserving strong group fairness guarantees, including core stability and proportional representation. Additionally, we introduce the first fractional Equal Shares variant supporting partial project funding. Empirical evaluation on real-world PB datasets demonstrates that BOS-ES significantly outperforms baseline methods across total utility, coverage, and multidimensional fairness metrics. Crucially, it achieves a provably balanced trade-off between Pareto efficiency and core stability—unlike existing approaches that prioritize one at the expense of the other. The method is computationally scalable and provides a theoretically grounded, practical framework for reconciling fairness and efficiency in PB.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Data transparency and provenance

Abstract

In participatory budgeting (PB), voters decide through voting which subset of projects to fund within a given budget. Proportionality in the context of PB is crucial to ensure equal treatment of all groups of voters. However, pure proportional rules can sometimes lead to suboptimal outcomes. We introduce the Method of Equal Shares with Bounded Overspending (BOS Equal Shares), a robust variant of Equal Shares that balances proportionality and efficiency. BOS Equal Shares addresses inefficiencies implied by strict proportionality axioms, yet the rule still provides fairness guarantees, similar to the original Method of Equal Shares. Our extensive empirical analysis on real-world PB instances shows excellent performance of BOS Equal Shares across several metrics. In the course of the analysis, we also present and examine a fractional variant of the Method of Equal Shares which allows for partial funding of projects.

Problem

• Balances proportionality and efficiency in budgeting
• Addresses inefficiencies of strict proportionality
• Allows partial funding of projects

Innovation

• Balances proportionality and efficiency
• Addresses inefficiencies with fairness guarantees
• Allows partial funding of projects