# The Core of the Participatory Budgeting Problem

arXiv: https://arxiv.org/abs/1610.03474 · HTML: https://mlsanity.com/paper/1610.03474/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Oct 2016.

## Built on by (most cited first, 14 of 14)

- [Proportional Aggregation of Preferences for Sequential Decision Making](https://mlsanity.com/paper/2306.14858/) (2023)
- [Generative Social Choice: The Next Generation](https://mlsanity.com/paper/2505.22939/) (2025)
- [Method of Equal Shares with Bounded Overspending](https://mlsanity.com/paper/2409.15005/) (2024)
- [Core-Stable Committees under Restricted Domains](https://mlsanity.com/paper/2108.01987/) (2021)
- [Bridging Voting and Deliberation with Algorithms: Field Insights from vTaiwan and Kultur Komitee](https://mlsanity.com/paper/2502.05017/) (2025)
- [Adversarial Robustness in Distributed Quantum Machine Learning](https://mlsanity.com/paper/2508.11848/) (2025)
- [What Should We Optimize in Participatory Budgeting? An Experimental Study](https://mlsanity.com/paper/2111.07308/) (2021)
- [Characterization of Group-Fair Social Choice Rules under Single-Peaked Preferences](https://mlsanity.com/paper/2207.07984/) (2022)
- [Harm Ratio: A Novel and Versatile Fairness Criterion](https://mlsanity.com/paper/2410.02977/) (2024)
- [Fair Transit Stop Placement: A Clustering Perspective and Beyond](https://mlsanity.com/paper/2602.06776/) (2026)
- [Strengthening Full Justified Representation: Efficient Verification and Computation](https://mlsanity.com/paper/2608.11500/) (2026)
- [Participatory Budgeting with Donations and Diversity Constraints](https://mlsanity.com/paper/2104.15075/) (2021)
- [Fairness in the Multi-Secretary Problem](https://mlsanity.com/paper/2511.23097/) (2025)
- [Procedural Fairness in Multi-Agent Bandits](https://mlsanity.com/paper/2601.10600/) (2026)

## Abstract (arXiv)

In participatory budgeting, communities collectively decide on the allocation of public tax dollars for local public projects. In this work, we consider the question of fairly aggregating the preferences of community members to determine an allocation of funds to projects. This problem is different from standard fair resource allocation because of public goods: The allocated goods benefit all users simultaneously. Fairness is crucial in participatory decision making, since generating equitable outcomes is an important goal of these processes. We argue that the classic game theoretic notion of core captures fairness in the setting. To compute the core, we first develop a novel characterization of a public goods market equilibrium called the Lindahl equilibrium, which is always a core solution. We then provide the first (to our knowledge) polynomial time algorithm for computing such an equilibrium for a broad set of utility functions; our algorithm also generalizes (in a non-trivial way) the well-known concept of proportional fairness. We use our theoretical insights to perform experiments on real participatory budgeting voting data. We empirically show that the core can be efficiently computed for utility functions that naturally model our practical setting, and examine the relation of the core with the familiar welfare objective. Finally, we address concerns of incentives and mechanism design by developing a randomized approximately dominant-strategy truthful mechanism building on the exponential mechanism from differential privacy.