Mixed Voting Rules for Participatory Budgeting

2026-06-22

AI Summary

Participatory budgeting often struggles to balance utilitarian welfare and proportional representation. This work proposes a novel hybrid voting rule that, for the first time, adapts the concept of mixed-member electoral systems to this setting by sequentially combining rules such as Greedy and Method of Equal Shares (MES). Projects are selected iteratively according to their budget shares, with voters’ effective budgets dynamically adjusted for subsequent rounds. The proposed enhanced MES mechanism, grounded in additive satisfaction functions, offers theoretical approximation guarantees under strong proportionality axioms like EJR+. Formal analysis demonstrates its superiority over natural proportional baselines, and empirical evaluation on real-world datasets confirms its effectiveness in achieving a balanced trade-off between utilitarian efficiency and proportionality—further improved through refined implementation details.

Abstract

Designing and analyzing voting rules for Participatory Budgeting (PB) elections is an active research area in computational social choice. Many PB voting rules aim to optimize a specific objective. For instance, the ubiquitous Greedy rule attempts to maximize utilitarian welfare, while the Method of Equal Shares (MES) aims to achieve proportional representation. However, it is often desirable to achieve good outcomes on multiple objectives rather than a close-to-perfect outcome for one. Inspired by mixed-member systems for parliamentary elections, we introduce mixed voting rules for PB. These are composed of a sequence of two or more rules that can each spend some fraction of the overall budget in order to add projects to the set selected by earlier rules. We develop a theoretical framework for formulating and analyzing mixed PB voting rules, and explore how existing rules can be adapted to this framework. We particularly focus on MES and its potential to address imbalances in representation created by earlier rules. We propose different ways to adjust MES voter budgets based on how satisfied voters are with previously chosen projects, and examine how well the resulting rules approximate well-known proportionality axioms such as EJR+. In particular, we show that one of these methods improves upon a natural proportionality baseline. We also extend our main positive result to general additive satisfaction functions. We complement our theoretical results with an extensive empirical analysis of real-world PB elections. Our experiments show that mixed rules can achieve favorable trade-offs between utilitarian welfare and proportionality. We identify several refinements that further improve their performance, and apply our framework to PB rules beyond Greedy and MES.

Problem

• Participatory Budgeting
• Voting Rules
• Proportionality
• Utilitarian Welfare
• Mixed Voting Systems

Innovation

• mixed voting rules
• participatory budgeting
• proportionality
• Method of Equal Shares
• EJR+