Participatory Budgeting Project Strength via Candidate Control

TL;DR

The paper investigates constructive and destructive candidate control in participatory budgeting, showing that while many PB rules are computationally hard to manipulate (NP-hard or beyond) under addition or deletion of projects, there exist efficient algorithms for natural cases such as GreedyAV with restricted costs. It provides a comprehensive reduction-based complexity landscape across GreedyAV, GreedyCost, Phragmén, and Equal-Shares, including polynomial-time DP solutions when costs are unary or uniform. Beyond theory, it introduces practical performance measures based on candidate control and validates them with extensive experiments on real PB data, offering insights into project rivalry, closeness to funding, and comparative behavior of PB rules. The results have implications for robustness, explainability, and policy design in participatory budgeting processes, informing both organizers and proposers about potential vulnerabilities and strategies. Overall, the work bridges computational social choice theory with PB practice, highlighting both fundamental limits and actionable analyses for evaluating project performance.

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 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.

Figures (13)

• Figure 1: An illustration of the election instance created in the proof of \ref{['thm:Phragmen:CCDC:NPh']}.
• Figure 2: An illustration of the election instance constructed in the proof of \ref{['thm:Phragmen:DCAC:NPh']}.
• Figure 3: The distribution of projects according to their optimal control size. Each bar represents one rule and is partitioned into five parts whose sizes correspond to the number of projects that require $r\in\{0,1,2,3,4+\}$ deletions to get funded. The part with winning projects is always the darkest, and the part for projects with $r \geq 4$ is the lightest.
• Figure 4: The ratio between the project's cost and the sum of costs of projects in the cheapest possible set of projects that makes a given project winning. The interesting projects are labeled with their name, and each project $p$ is plotted for every rule $f$ (unless $p\in f(E)$). Instance: Warsaw, 2023.
• Figure 5: The probability of being funded for each initially losing project after removing $r\in\{1,2,3\}$ projects. The projects are ordered according to their winning probability for $r=1$. The used rule is GreedyAV, and the depicted instance is Warsaw, Ursynow, 2019.

Theorems & Definitions (34)

• Definition 1
• Example 1
• Theorem 1
• proof
• Claim 1
• proof
• Proposition 1
• proof
• Claim 2
• Theorem 2