Coordinating Monetary Contributions in Participatory Budgeting

TL;DR

This paper introduces a formal framework for coordinating funding and project selection in participatory budgeting, analyzing axioms, objectives, and computational complexity, including special cases with tractable solutions.

Contribution

It formalizes a comprehensive model for participatory budgeting, explores axioms and objectives, and identifies tractable cases under specific valuation restrictions.

Findings

Welfare maximization admits an FPTAS.

Participation constraints lead to inapproximability in general.

Tractable solutions exist for laminar and symmetric valuations.

Abstract

We formalize a framework for coordinating funding and selecting projects, the costs of which are shared among agents with quasi-linear utility functions and individual budgets. Our model contains the classical discrete participatory budgeting model as a special case, while capturing other useful scenarios. We propose several important axioms and objectives and study how well they can be simultaneously satisfied. We show that whereas welfare maximization admits an FPTAS, welfare maximization subject to a natural and very weak participation requirement leads to a strong inapproximability. This result is bypassed if we consider some natural restricted valuations, namely laminar single-minded valuations and symmetric valuations. Our analysis for the former restriction leads to the discovery of a new class of tractable instances for the Set Union Knapsack problem, a classical problem in combinatorial optimization.