Strategic Cost Selection in Participatory Budgeting

TL;DR

This paper models strategic cost reporting in approval-based participatory budgeting as PB games where proposers set prices to maximize profit subject to delivery costs and budget, and analyzes Nash equilibria under basic and MES/Phragmén rules. It establishes that MES-Cost with cost utilities always admits a Nash equilibrium, while AV/Cost, Phragmén, and MES with approval utilities can lack equilibria depending on tie-breaking; it also provides polynomial-time methods to compute AV/Cost–NE and MES–variants in several settings. The authors complement theory with experiments on real PB data, illustrating how different rules yield distinct cost distributions and equilibrium behaviors, and they study dynamics to approximate equilibria in practice. The findings offer guidance for PB rule design by highlighting potential pathologies and showing when equilibria can be efficiently achieved, with implications for fairness and budget efficiency in city budgeting.

Abstract

We study strategic behavior of project proposers in the context of approval-based participatory budgeting (PB). In our model we assume that the votes are fixed and known and the proposers want to set as high project prices as possible, provided that their projects get selected and the prices are not below the minimum costs of their delivery. We study the existence of pure Nash equilibria (NE) in such games, focusing on the AV/Cost, Phragmén, and Method of Equal Shares rules. Furthermore, we report an experimental study of strategic cost selection on real-life PB election data.

Figures (7)

• Figure 1: Examples of plurality (left), party list (middle), and unrestricted (right) preferences. Projects are depicted as boxes. Each voter approves those projects that are drawn directly above.
• Figure 2: Illustration of the PB game from the proof of \ref{['pro:phrag-laminar-no-ne']}. The projects are depicted as boxes. Each voter approves those projects that are drawn directly above him or her (and are crossed by the dotted line).
• Figure 3: Approval sets of projects $p_1, p_2, p_3$, and $p_4$. Here, each vertex represents a single voter.
• Figure 4: Winning and losing margins in real-life PB. Each bar shows a single project (the projects are ordered by their approval score, shown on the ${x}$ axis). Green and red ones give best responses (where green means a winning margin and red means a losing one). Black rectangles show the original costs, with budget $1 011$k PLN for Wesola and 250k EUR for Kleine Wereld.
• Figure 5: Strategy profiles after ${10 \ 000}$ iterations of our dynamics. Bars represent the projects ( in the order of their approval score, depicted on the ${x}$ axis). The green bars show final costs of the winning projects (the brighter part emphasizes the increase, as compared to the original cost). The red bars show final costs of losing projects. Black outlines denote the original costs of the projects. Black triangles mark the originally winning projects. Brown circles denote the equilibrium costs (for rules where we can compute it).

Theorems & Definitions (40)

• Remark 1
• Definition 3
• Example 1
• Definition 6: Approval-Proportional Strategy Profile
• Proposition 1
• proof
• Proposition 2
• proof : Proof Sketch
• proof
• Proposition 3