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Truth-Revealing Participatory Budgeting

Qishen Han, Artem Ivaniuk, Edith Elkind, Lirong Xia

TL;DR

This paper introduces an epistemic framework for participatory budgeting in which project qualities are latent and voters receive noisy signals. It analyzes how well common PB rules can reveal the highest-quality projects, deriving asymptotic performance results under unit costs (where many rules approach optimality) and general costs (where performance is bounded and worsened by dispersion). It also initiates incentive analysis, showing informative voting is rarely a Bayes-Nash equilibrium under broad conditions, and corroborates theoretical insights with large-scale experiments, revealing MES+AV often yields strong truth-revealing performance. The work advances understanding of information aggregation in multi-project budgeting and points to avenues for integrating epistemic and axiomatic objectives in PB design.

Abstract

Participatory Budgeting (PB) is commonly studied from an axiomatic perspective, where the aim is to design procedurally fair and economically efficient rules for voters with full information regarding their preferences. In contrast, we take an epistemic perspective and consider a framework where PB projects have different levels of underlying quality, indicating how well the project will take effect, which cannot be directly observed before implementation. Agents with noisy information cast votes to aggregate their information, and aim to elect a high-quality set of projects. We evaluate the performance of common PB rules by measuring the expected utility of their outcomes, compared to the optimal set of projects. We find that the quality of approximation improves as the range of project costs shrinks. When projects have unit cost, these common rules can identify the ``best'' set with probability converging to 1. We also study whether strategic agents have incentives to honestly convey their information in the vote. We find that it happens only under very restrictive conditions. We also run numerical experiments to examine the performance of different rules empirically and support our theoretical findings.

Truth-Revealing Participatory Budgeting

TL;DR

This paper introduces an epistemic framework for participatory budgeting in which project qualities are latent and voters receive noisy signals. It analyzes how well common PB rules can reveal the highest-quality projects, deriving asymptotic performance results under unit costs (where many rules approach optimality) and general costs (where performance is bounded and worsened by dispersion). It also initiates incentive analysis, showing informative voting is rarely a Bayes-Nash equilibrium under broad conditions, and corroborates theoretical insights with large-scale experiments, revealing MES+AV often yields strong truth-revealing performance. The work advances understanding of information aggregation in multi-project budgeting and points to avenues for integrating epistemic and axiomatic objectives in PB design.

Abstract

Participatory Budgeting (PB) is commonly studied from an axiomatic perspective, where the aim is to design procedurally fair and economically efficient rules for voters with full information regarding their preferences. In contrast, we take an epistemic perspective and consider a framework where PB projects have different levels of underlying quality, indicating how well the project will take effect, which cannot be directly observed before implementation. Agents with noisy information cast votes to aggregate their information, and aim to elect a high-quality set of projects. We evaluate the performance of common PB rules by measuring the expected utility of their outcomes, compared to the optimal set of projects. We find that the quality of approximation improves as the range of project costs shrinks. When projects have unit cost, these common rules can identify the ``best'' set with probability converging to 1. We also study whether strategic agents have incentives to honestly convey their information in the vote. We find that it happens only under very restrictive conditions. We also run numerical experiments to examine the performance of different rules empirically and support our theoretical findings.
Paper Structure (39 sections, 22 theorems, 148 equations, 15 figures, 3 tables)

This paper contains 39 sections, 22 theorems, 148 equations, 15 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Our Contribution
  3. Related Work and Discussion
  4. Preliminaries
  5. An Epistemic Model for PB
  6. Performance of PB Rules
  7. Strategic Behavior in Epistemic PB
  8. Two Alternatives: Rarely a BNE
  9. Unit Cost: A Restrictive Necessary Condition
  10. Experiments
  11. Future Work
  12. Definition of Voting Rules.
  13. Proof of Theorem \ref{['thm:unit_positive']}
  14. Complimentary Proof for Theorem \ref{['thm:general_impossibility']}
  15. Construction for $v^C$.
  16. ...and 24 more sections

Key Result

Theorem 1

In the unit-cost setting, for any quality dominant environment, every voting rule $r \in \{\textrm{AV}, \textrm{Greedy Cover}, \textrm{Phragm\'{e}n}, \textrm{MES}\textrm{+}\textrm{AV}, \textrm{MES} \textrm{+} \textrm{Phragm\'{e}n},$$\textrm{PAV}\}$ satisfies $\lim_{n\to\infty} \mathcal{P}(r, n) = 1

Figures (15)

  • Figure 1: Performance with unit cost ($\alpha = 1$)
  • Figure 2: Performance with general cost ($\alpha = 5$)
  • Figure 3: Performance on different $\alpha$ ($\textrm{AV}$ rule, $B = 7$)
  • Figure 4: Performance on the number of agents, normal utility.
  • Figure 5: Performance under different budgets, normal utility
  • ...and 10 more figures

Theorems & Definitions (57)

  • Example 1
  • Example 2
  • Definition 1
  • Theorem 1
  • Theorem 2
  • proof
  • Definition 2
  • Corollary 1
  • Theorem 3
  • Theorem 4
  • ...and 47 more