Submodular Participatory Budgeting

TL;DR

This paper extends participatory budgeting to settings where voter utilities are monotone submodular, capturing diminishing returns and negative interactions between projects. It analyzes three preference elicitation methods—group based ranking-by-marginal-values, group based ranking-by-values, and threshold approval votes—under implicit utilitarian voting, providing distortion bounds that depend on the number of alternatives $m$ and the curvature $c$ of the submodular utilities. The main results show $O(\log m\sqrt{m}/(1-c))$ distortion for the ranking-based methods and $O(\log m/(1-c))$ for threshold approvals, with $c=0$ recovering $O(\log m)$ and improving over prior $O(\log^2 m)$ for additive utilities. These findings guide the design of participatory budgeting mechanisms when project interactions matter, and point to future work on extending to positive interactions and exploring deterministic strategies.

Abstract

Participatory budgeting refers to the practice of allocating public resources by collecting and aggregating individual preferences. Most existing studies in this field often assume an additive utility function, where each individual holds a private utility for each candidate project, and the total utility of a set of funded projects is simply the sum of the utilities of all projects. We argue that this assumption does not always hold in reality. For example, building two playgrounds in the same neighborhood does not necessarily lead to twice the utility of building a single playground. To address this, we extend the existing study by proposing a submodular participatory budgeting problem, assuming that the utility function of each individual is a monotone and submodular function over funded projects. We propose and examine three preference elicitation methods, including \emph{ranking-by-marginal-values}, \emph{ranking-by-values} and \emph{threshold approval votes}, and analyze their performances in terms of distortion. Notably, if the utility function is addicative, our aggregation rule designed for threshold approval votes achieves a better distortion than the state-of-the-art approach.

Theorems & Definitions (10)

• Lemma 1
• Lemma 2
• Lemma 3
• Theorem 1
• Lemma 4
• Lemma 5
• Theorem 2
• Lemma 6
• Lemma 7
• Theorem 3