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Detecting and taking Project Interactions into account in Participatory Budgeting

Martin Durand, Fanny Pascual

TL;DR

This work extends participatory budgeting to account for project interactions by detecting synergies from knapsack ballots using co-occurrence statistics and a Möbius-transform based utility $u_M$. It formulates axioms for utility functions under synergies and analyzes three aggregation rules (sum, product, min), proving the associated optimization problems are NP-hard and offering a branch-and-bound solver. Empirical evaluation on real knapsack voting data demonstrates the feasibility and impact of incorporating synergies, showing that ignoring interactions can lead to significantly different bundles. The approach provides a principled framework to capture complementarities and substitutions among projects, with potential to improve fairness and efficiency in public decision-making.

Abstract

The aim of this paper is to introduce models and algorithms for the Participatory Budgeting problem when projects can interact with each other. In this problem, the objective is to select a set of projects that fits in a given budget. Voters express their preferences over the projects and the goal is then to find a consensus set of projects that does not exceed the budget. Our goal is to detect such interactions thanks to the preferences expressed by the voters. Through the projects selected by the voters, we detect positive and negative interactions between the projects by identifying projects that are consistently chosen together. In presence of project interactions, it is preferable to select projects that interact positively rather than negatively, all other things being equal. We introduce desirable properties that utility functions should have in presence of project interactions and we build a utility function which fulfills the desirable properties introduced. We then give axiomatic properties of aggregation rules, and we study three classical aggregation rules: the maximization of the sum of the utilities, of the product of the utilities, or of the minimal utility. We show that in the three cases the problems solved by these rules are NP-hard, and we propose a branch and bound algorithm to solve them. We conclude the paper by experiments.

Detecting and taking Project Interactions into account in Participatory Budgeting

TL;DR

This work extends participatory budgeting to account for project interactions by detecting synergies from knapsack ballots using co-occurrence statistics and a Möbius-transform based utility . It formulates axioms for utility functions under synergies and analyzes three aggregation rules (sum, product, min), proving the associated optimization problems are NP-hard and offering a branch-and-bound solver. Empirical evaluation on real knapsack voting data demonstrates the feasibility and impact of incorporating synergies, showing that ignoring interactions can lead to significantly different bundles. The approach provides a principled framework to capture complementarities and substitutions among projects, with potential to improve fairness and efficiency in public decision-making.

Abstract

The aim of this paper is to introduce models and algorithms for the Participatory Budgeting problem when projects can interact with each other. In this problem, the objective is to select a set of projects that fits in a given budget. Voters express their preferences over the projects and the goal is then to find a consensus set of projects that does not exceed the budget. Our goal is to detect such interactions thanks to the preferences expressed by the voters. Through the projects selected by the voters, we detect positive and negative interactions between the projects by identifying projects that are consistently chosen together. In presence of project interactions, it is preferable to select projects that interact positively rather than negatively, all other things being equal. We introduce desirable properties that utility functions should have in presence of project interactions and we build a utility function which fulfills the desirable properties introduced. We then give axiomatic properties of aggregation rules, and we study three classical aggregation rules: the maximization of the sum of the utilities, of the product of the utilities, or of the minimal utility. We show that in the three cases the problems solved by these rules are NP-hard, and we propose a branch and bound algorithm to solve them. We conclude the paper by experiments.
Paper Structure (18 sections, 11 theorems, 8 equations, 5 figures, 1 table)

This paper contains 18 sections, 11 theorems, 8 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related work
  3. Our approach to interaction detection
  4. Overview of our results
  5. Preliminaries
  6. Axioms for utility functions
  7. A utility function taking synergies into account
  8. A function using Möbius transforms: $u_M$
  9. Properties of $u_M$, and remarks on its computation
  10. Axioms for budgeting methods
  11. Complexity
  12. A branch and bound algorithm
  13. Description of the algorithm
  14. Experiments
  15. Quality of the heuristic.
  16. ...and 3 more sections

Key Result

Proposition 1

The utility function $u_M$ fulfills cost consistency, super-set monotonicity, the effect of positive synergies property, the effect of negative synergies property, regrouping monotonicity and cost aware neutrality. It also fulfills the strong effect of positive synergies property if for each project

Figures (5)

  • Figure 1: Example with $l=4$
  • Figure 2: First budgeting scenario $E$
  • Figure 3: Second budgeting scenario $E'$
  • Figure 4: First budgeting scenario $E$
  • Figure 5: Second budgeting scenario $E'$

Theorems & Definitions (36)

  • Example 1
  • Example 2
  • Example 3
  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Example 4
  • ...and 26 more