Participatory Budgeting Project Strength via Candidate Control

Piotr Faliszewski, Lukasz Janeczko, Dusan Knop, Jan Pokorný, Simon Schierreich, Mateusz Sluszniak, Krzysztof Sornat

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 Phragmén and 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.