Evaluation of Project Performance in Participatory Budgeting

TL;DR

We address the problem of evaluating losing projects in participatory budgeting by formalizing measures that quantify how close a losing project is to winning under AV, Phragmén, and Equal-Shares rules. The paper introduces cost-reduction, add-approvals, add-singletons, and rivalry-reduction measures, and develops fast, practical algorithms (including FPT methods) to compute them on large real-world PB data from Pabulib, often alongside the PB rules themselves. Empirical results on hundreds of PB instances show strong correlations among some measures and meaningful differences between others, illustrating how different actions affect a project’s chances and how to construct informative information packages for voters and proposers. A Wieliczka 2023 Green Million case study demonstrates how these measures can guide campaign planning and post-election explanations, with Equal-Shares used in practice in real elections. The work offers practical, scalable tools to enhance transparency and participant understanding in PB by linking theoretical margins of victory to actionable strategies.

Abstract

We study ways of evaluating the performance of losing projects in participatory budgeting (PB) elections by seeking actions that would have led to their victory. We focus on lowering the projects' costs, obtaining additional approvals for them, and asking supporters to refrain from approving other projects: The larger a change is needed, the less successful is the given project. We seek efficient algorithms for computing our measures and we analyze and compare them experimentally. We focus on the greedyAV, Phragmén, and Equal-Shares PB rules.

Figures (13)

• Figure 1: Correlation plots where each point is one project. Measures are normalized so that 1 denotes no change and 0 denotes a maximal-size change.
• Figure 2: Line plots showing how the funding probability of a project develops from $0$ to $1$ when increasing its approval score by adding approvals uniformly at random to existing voters. The red area goes until the $\mathrm{optimist\hbox{-}add}$ value and the green area extends from the ${{\mathrm{pessimist\hbox{-}add}}}$ value.
• Figure 3: Behavior of two projects when adding voters who only support the project, taken from Warsaw 2023 (Praga-Polnoc, in blue) and Warsaw 2017 (Goclaw, in orange).
• Figure 4: Line plots showing how the funding probability of a project develops if we remove rivalry approvals from its supporters selected uniformly at random (each line corresponds to a single project; all non-funded projects are shown).
• Figure 5: Information on the Wieliczka 2023 Green Million election.

Theorems & Definitions (24)

• Definition 2.1
• Definition 3.1
• Proposition 3.1
• Definition 3.2
• Proposition 3.2
• Theorem 3.3
• Theorem 3.4
• proof : Proof sketch (Phragmén)
• Definition 3.5
• Proposition 3.5