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 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.

翻译：本文研究参与式预算选举中候选人控制问题的计算复杂性。建设性候选人控制的目标是通过在选举中增加或删除候选人，确保特定候选人获胜（在破坏性场景中，目标则是阻止特定候选人获胜）。我们证明，对于包括Phragmén法和等额分配法在内的多种参与式预算投票规则，此类控制问题均具有NP难解性，但也存在具有多项式时间算法的自然情形（例如针对GreedyAV规则及以一元编码表示成本的项目）。我们进一步论证，通过删除候选人进行控制是评估初始落选项目表现（即强度）的有效工具，并通过实验验证了这一观点。