Participatory Budgeting Project Strength via Candidate Control

TL;DR

This paper analyzes the computational complexity of candidate control in participatory budgeting, showing NP-hardness for many voting rules but identifying some cases with efficient algorithms, and demonstrates the practical utility of candidate deletion for project assessment.

Contribution

It provides a complexity analysis of candidate control in participatory budgeting and introduces experimental validation of candidate deletion as a project strength measure.

Findings

NP-hardness for many voting rules including Phragmén and Method of Equal Shares

Polynomial-time algorithms for GreedyAV and unary-encoded costs

Candidate deletion useful for assessing project strength

Abstract

We study the complexity of candidate control in participatory budgeting elections. The goal of constructive candidate control is to ensure that a given candidate wins by either adding or deleting candidates from the election (in the destructive setting, the goal is to prevent a given candidate from winning). We show that such control problems are NP-hard to solve for many participatory budgeting voting rules, including Phragm\'en and Method of Equal Shares, but there are natural cases with polynomial-time algorithms (e.g., for the GreedyAV rule and projects with costs encoded in unary). We also argue that control by deleting candidates is a useful tool for assessing the performance (or, strength) of initially losing projects, and we support this view with experiments.