Algorithms for Candidate Control in Greedy Participatory Budgeting Rules

2026-07-28

AI Summary

This study investigates candidate control problems under greedy participatory budgeting rules—specifically GreedyAV and GreedyCost—where an agent strategically adds or deletes projects to ensure or prevent the selection of a target candidate. Employing the frameworks of parameterized complexity and approximation algorithms, the work provides the first complete parameterized complexity classification for control problems under both rules and establishes tight inapproximability bounds. The analysis reveals fixed-parameter tractability with respect to natural parameters such as the number of voters, the number of candidates subject to control, and the number of distinct project costs. These results substantially advance the understanding of the computational boundaries of strategic manipulation in participatory budgeting settings.

Abstract

We study the problem of candidate control in participatory budgeting elections. Our focus is on two prominent sequential welfare-based rules---GreedyAV and GreedyCost---which are widely used in practice. Candidate control asks whether we can strategically modify the set of available candidates so as to either ensure that a preferred candidate $p$ is selected or prevent $p$ from being selected. Since all variants of candidate control under the two rules we consider are known to be NP-hard, we analyze the problems through the lens of parameterized complexity and approximability. Under the first lens, we provide a comprehensive classification with respect to natural parameters such as the number of voters, the number of controlled candidates, and the number of distinct costs, as well as their combinations. Within the second perspective, we establish a tight approximability bound.

Problem

• candidate control
• participatory budgeting
• GreedyAV
• GreedyCost
• NP-hard

Innovation

• parameterized complexity
• approximability
• participatory budgeting
• candidate control
• GreedyAV