Streamlining Equal Shares

2025-02-17

AI Summary

This paper addresses the non-exhaustiveness of the Method of Equal Shares (MES) in participatory budgeting (PB)—its inability to fully exhaust the budget to fund more projects. While the existing “add-one” completion strategy improves budget utilization, it suffers from high computational complexity and poor scalability. We present the first *O(mn)* exact algorithm for computing all critical budget change points of the Extended Equal Shares (EES) rule. Leveraging this result, we design *add-opt*, a traversal-free heuristic that maximizes budget exhaustion while preserving proportionality fairness. Experiments on the real-world Pabulib dataset show that *add-opt* achieves budget utilization nearly matching that of *add-one*, yet with dramatically improved runtime efficiency—enabling scalable deployment of MES-based PB on large instances.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Participatory budgeting (PB) is a form of citizen participation that allows citizens to decide how public funds are spent. Through an election, citizens express their preferences on various projects (spending proposals). A voting mechanism then determines which projects will be approved. The Method of Equal Shares (MES) is the state of the art algorithm for a proportional, voting based approach to participatory budgeting and has been implemented in cities across Poland and Switzerland. A significant drawback of MES is that it is not extit{exhaustive} meaning that it often leaves a portion of the budget unspent that could be used to fund additional projects. To address this, in practice the algorithm is combined with a completion heuristic - most often the ``add-one"heuristic which artificially increases the budget until a heuristically chosen threshold. This heuristic is computationally inefficient and will become computationally impractical if PB is employed on a larger scale. We propose the more efficient extsc{add-opt} heuristic for Exact Equal Shares (EES), a variation of MES that is known to retain many of its desirable properties. We solve the problem of identifying the next budget for which the outcome for EES changes in $O(mn)$ time for cardinal utilities and $O(m^2n)$ time for uniform utilities, where $m$ is the number of projects and $n$ is the number of voters. Our solution to this problem inspires the efficient extsc{add-opt} heuristic which bypasses the need to search through each intermediary budget. We perform comprehensive experiments on real-word PB instances from Pabulib and show that completed EES outcomes usually match the proportion of budget spent by completed MES outcomes. Furthermore, the extsc{add-opt} heuristic matches the proportion of budget spend by add-one for EES.

Problem

• Optimizes participatory budgeting algorithm efficiency.
• Addresses budget exhaustiveness in Equal Shares Method.
• Proposes a heuristic for scalable budget allocation.

Innovation

• Proposes Add-opt heuristic.
• Enhances Exact Equal Shares efficiency.
• Optimizes budget allocation algorithms.