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arXiv · 2601.16511

Participatory Budgeting Project Strength via Candidate Control

Piotr Faliszewski·Łukasz Janeczko·Dušan Knop·Jan Pokorný·Šimon Schierreich·Mateusz Słuszniak·Krzysztof Sornat
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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.

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Piotr Faliszewski, Łukasz Janeczko, Dušan Knop, Jan Pokorný, Šimon Schierreich, Mateusz Słuszniak, Krzysztof Sornat. 2026-01-23. Participatory Budgeting Project Strength via Candidate Control. https://arxiv.org/abs/2601.16511

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