# Proportional Participatory Budgeting with Additive Utilities

arXiv: https://arxiv.org/abs/2008.13276 · HTML: https://mlsanity.com/paper/2008.13276/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2020.

## Built on by (most cited first, 30 of 37)

- [Generative Social Choice](https://mlsanity.com/paper/2309.01291/) (2023)
- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Temporal Fairness in Multiwinner Voting](https://mlsanity.com/paper/2312.04417/) (2023)
- [Proportional Fairness in Clustering: A Social Choice Perspective](https://mlsanity.com/paper/2310.18162/) (2023)
- [Generative Social Choice: The Next Generation](https://mlsanity.com/paper/2505.22939/) (2025)
- [Online Approval Committee Elections](https://mlsanity.com/paper/2202.06830/) (2022)
- [Strengthening Proportionality in Temporal Voting](https://mlsanity.com/paper/2505.22513/) (2025)
- [Proportionally Representative Clustering](https://mlsanity.com/paper/2304.13917/) (2023)
- [Generative AI voting: fair collective choice is resilient to LLM biases and inconsistencies](https://mlsanity.com/paper/2406.11871/) (2024)
- [Proportional Fairness in Non-Centroid Clustering](https://mlsanity.com/paper/2410.23273/) (2024)
- [Method of Equal Shares with Bounded Overspending](https://mlsanity.com/paper/2409.15005/) (2024)
- [Beyond RLHF and NLHF: Population-Proportional Alignment under an Axiomatic Framework](https://mlsanity.com/paper/2506.05619/) (2025)
- [Random Rank: The One and Only Strategyproof and Proportionally Fair Randomized Facility Location Mechanism](https://mlsanity.com/paper/2205.14798/) (2022)
- [Proportional Representation in Metric Spaces and Low-Distortion Committee Selection](https://mlsanity.com/paper/2312.10369/) (2023)
- [Abductive and Contrastive Explanations for Scoring Rules in Voting](https://mlsanity.com/paper/2408.12927/) (2024)
- [Full Proportional Justified Representation](https://mlsanity.com/paper/2501.12015/) (2025)
- [Bridging Voting and Deliberation with Algorithms: Field Insights from vTaiwan and Kultur Komitee](https://mlsanity.com/paper/2502.05017/) (2025)
- [The Price of Proportional Representation in Temporal Voting](https://mlsanity.com/paper/2605.11157/) (2026)
- [Maxmin Participatory Budgeting](https://mlsanity.com/paper/2204.13923/) (2022)
- [Upgrading Democracies with Fairer Voting Methods](https://mlsanity.com/paper/2505.14349/) (2025)
- [Metritocracy: Representative Metrics for Lite Benchmarks](https://mlsanity.com/paper/2506.09813/) (2025)
- [Indivisible Participatory Budgeting under Weak Rankings](https://mlsanity.com/paper/2207.07981/) (2022)
- [Selecting the Most Conflicting Pair of Candidates](https://mlsanity.com/paper/2405.05870/) (2024)
- [Harm Ratio: A Novel and Versatile Fairness Criterion](https://mlsanity.com/paper/2410.02977/) (2024)
- [Proportional Selection in Networks](https://mlsanity.com/paper/2502.03545/) (2025)
- [Proportional Committee Elections with Positive and Negative Votes](https://mlsanity.com/paper/2503.01985/) (2025)
- [Fair Voting Methods as a Catalyst for Democratic Resilience: A Trilogy on Legitimacy, Impact and AI Safeguarding](https://mlsanity.com/paper/2512.17461/) (2025)
- [Large Language Models for Designing Participatory Budgeting Rules](https://mlsanity.com/paper/2602.09349/) (2026)
- [Strengthening Full Justified Representation: Efficient Verification and Computation](https://mlsanity.com/paper/2608.11500/) (2026)
- [The Distortion of Binomial Voting Defies Expectation](https://mlsanity.com/paper/2306.15657/) (2023)

## Abstract (arXiv)

We study voting rules for participatory budgeting, where a group of voters collectively decides which projects should be funded using a common budget. We allow the projects to have arbitrary costs, and the voters to have arbitrary additive valuations over the projects. We formulate an axiom (Extended Justified Representation, EJR) that guarantees proportional representation to groups of voters with common interests. We propose a simple and attractive voting rule called the Method of Equal Shares that satisfies this axiom for arbitrary costs and approval utilities, and that satisfies the axiom up to one project for arbitrary additive valuations. This method can be computed in polynomial time. In contrast, we show that the standard method for achieving proportionality in committee elections, Proportional Approval Voting (PAV), cannot be extended to work with arbitrary costs. Finally, we introduce a strengthened axiom (Full Justified Representation, FJR) and show that it is also satisfiable, though by a computationally more expensive and less natural voting rule.