Submodular Participatory Budgeting

TL;DR

This paper introduces a submodular utility model for participatory budgeting, proposing new preference elicitation methods and demonstrating improved distortion bounds over existing additive models.

Contribution

It extends participatory budgeting models to submodular utilities, proposes three preference elicitation methods, and analyzes their performance, including a novel aggregation rule with better distortion bounds.

Findings

Preference elicitation methods analyzed for submodular utilities

Aggregation rule for threshold approval votes outperforms existing methods in additive cases

Proposed methods achieve lower distortion in utility aggregation

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.