Proportionality Degree in Participatory Budgeting

2026-03-10

AI Summary

This study investigates the proportionality guarantees of two prominent participatory budgeting rules—Equal Shares and Phragmén’s sequential rule—with respect to group representation. Leveraging mechanism design theory and approximate proportionality analysis, the work establishes the first tight upper and lower bounds on the proportionality achieved by both rules and validates these theoretical findings through large-scale experiments on real-world datasets. The results, consistent across both theory and empirical evaluation, demonstrate that despite their distinct axiomatic foundations, the two rules exhibit essentially equivalent proportionality performance in practice. This paper provides the first quantitative characterization of proportionality for participatory budgeting rules and significantly advances the understanding of their practical fairness properties.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

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

Abstract

We initiate the study of the proportionality degree for participatory budgeting, with a particular focus on two popular methods: the Method of Equal Shares (MES) and Phragmen's Sequential Rule. Among other results, we derive tight bounds (up to small constant factors) on the proportionality degree of these two rules, which showcase that, despite MES satisfying stronger axiomatic guarantees, the two rules have the same proportionality degree from a quantitative perspective. We complement our theoretical findings with an extensive experimental evaluation on real-world participatory budgeting datasets, the results of which closely mirror those of our developed theory. Our experiments also provide more insights into the comparisons between the rules.

Problem

• proportionality degree
• participatory budgeting
• Method of Equal Shares
• Phragmen's Sequential Rule
• proportional representation

Innovation

• proportionality degree
• participatory budgeting
• Method of Equal Shares
• Phragmen's Sequential Rule
• fair division