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Exploring Welfare Maximization and Fairness in Participatory Budgeting

Gogulapati Sreedurga

Abstract

Participatory budgeting (PB) is a voting paradigm for distributing a divisible resource, usually called a budget, among a set of projects by aggregating the preferences of individuals over these projects. It is implemented quite extensively for purposes such as government allocating funds to public projects and funding agencies selecting research proposals to support. This PhD dissertation studies the welfare-related and fairness-related objectives for different PB models. Our contribution lies in proposing and exploring novel PB rules that maximize welfare and promote fairness, as well as, in introducing and investigating a range of novel utility notions, axiomatic properties, and fairness notions, effectively filling the gaps in the existing literature for each PB model. The thesis is divided into two main parts, the first focusing on dichotomous and the second focusing on ordinal preferences. Each part considers two cases: (i) the cost of each project is restricted to a single value and partial funding is not permitted and (ii) the cost of each project is flexible and may assume multiple values.

Exploring Welfare Maximization and Fairness in Participatory Budgeting

Abstract

Participatory budgeting (PB) is a voting paradigm for distributing a divisible resource, usually called a budget, among a set of projects by aggregating the preferences of individuals over these projects. It is implemented quite extensively for purposes such as government allocating funds to public projects and funding agencies selecting research proposals to support. This PhD dissertation studies the welfare-related and fairness-related objectives for different PB models. Our contribution lies in proposing and exploring novel PB rules that maximize welfare and promote fairness, as well as, in introducing and investigating a range of novel utility notions, axiomatic properties, and fairness notions, effectively filling the gaps in the existing literature for each PB model. The thesis is divided into two main parts, the first focusing on dichotomous and the second focusing on ordinal preferences. Each part considers two cases: (i) the cost of each project is restricted to a single value and partial funding is not permitted and (ii) the cost of each project is flexible and may assume multiple values.

Paper Structure

This paper contains 154 sections, 76 theorems, 91 equations, 17 figures, 10 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Landscape of PB Models
  3. Preferences in PB
  4. Costs in PB
  5. Objectives of PB
  6. Relating the Thesis to the State-of-the-Art
  7. Relevant Work and Research Gaps in the Literature
  8. Dichotomous Preferences - Restricted Costs
  9. Dichotomous Preferences - Flexible Costs
  10. Ordinal Preferences - Restricted Costs
  11. Welfare Maximization.
  12. Fairness.
  13. Ordinal Preferences - Flexible Costs
  14. Thesis Contributions and Overview
  15. Background
  16. ...and 139 more sections

Key Result

Theorem 3.1

The decision version of $\mathsf{MPB}$ is strongly $\mathsf{NP}$-hard.

Figures (17)

  • Figure 1: English Translation: You (both) have molded me in countless ways. You always stood by my side like true friends. All my accomplishments indeed belong to you. How else do I worship you and express my boundless love for you?
  • Figure 2: Participatory budgeting for government funding public projects.
  • Figure 3: Participatory budgeting for agencies funding research proposals.
  • Figure 4: Stylized example to illustrate preferences for \ref{['eg: preferences']}.
  • Figure 5: Stylized example to illustrate the need for egalitarian welfare in PB under dichotomous preferences and restricted costs.
  • ...and 12 more figures

Theorems & Definitions (178)

  • Example 1.1
  • Example 1.2
  • Definition 2.1: PB Rule under Restricted Costs
  • Definition 2.2: PB Rule under Flexible Costs
  • Example
  • Definition 2.3
  • Definition 2.4: $\boldsymbol{\mathsf{NP}\xspace}$-hard and $\boldsymbol{\mathsf{NP}\xspace}$-complete
  • Definition 2.5: Weakly $\boldsymbol{\mathsf{NP}\xspace}$-hard and Strongly $\boldsymbol{\mathsf{NP}\xspace}$-hard
  • Definition 2.6
  • Definition 2.7
  • ...and 168 more