Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fair Lotteries for Participatory Budgeting

Haris Aziz, Xinhang Lu, Mashbat Suzuki, Jeremy Vollen, Toby Walsh

TL;DR

The paper studies lotteries over participatory budgeting outcomes to achieve best-of-both-worlds fairness, balancing ex-ante fairness with ex-post fairness under budget constraints. It introduces BB1 to bound ex-post budget deviations when implementing fractional PB outcomes via lotteries and develops both exponential-time and polynomial-time algorithms (notably BW-GCR-PB and BW-MES-PB) to realize ex-ante Strong UFS alongside ex-post FJR, EJR, and BB1 in PB with binary utilities. The work shows fundamental incompatibilities (e.g., ex-ante GFS with ex-post JR) and delineates the feasibility frontier for BoBW fairness in general PB, providing rigorous proofs and constructive algorithms. The results have implications for designing fair, implementable PB mechanisms that respect budget constraints while guaranteeing meaningful representation for individuals and groups. Overall, the paper advances the integration of randomized mechanisms, budget feasibility, and ex-ante/ex-post fairness in the PB setting, with practical significance for deploying fair participatory budgeting processes.

Abstract

In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend -- the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.

Fair Lotteries for Participatory Budgeting

TL;DR

The paper studies lotteries over participatory budgeting outcomes to achieve best-of-both-worlds fairness, balancing ex-ante fairness with ex-post fairness under budget constraints. It introduces BB1 to bound ex-post budget deviations when implementing fractional PB outcomes via lotteries and develops both exponential-time and polynomial-time algorithms (notably BW-GCR-PB and BW-MES-PB) to realize ex-ante Strong UFS alongside ex-post FJR, EJR, and BB1 in PB with binary utilities. The work shows fundamental incompatibilities (e.g., ex-ante GFS with ex-post JR) and delineates the feasibility frontier for BoBW fairness in general PB, providing rigorous proofs and constructive algorithms. The results have implications for designing fair, implementable PB mechanisms that respect budget constraints while guaranteeing meaningful representation for individuals and groups. Overall, the paper advances the integration of randomized mechanisms, budget feasibility, and ex-ante/ex-post fairness in the PB setting, with practical significance for deploying fair participatory budgeting processes.

Abstract

In pursuit of participatory budgeting (PB) outcomes with broader fairness guarantees, we initiate the study of lotteries over discrete PB outcomes. As the projects have heterogeneous costs, the amount spent may not be equal ex ante and ex post. To address this, we develop a technique to bound the amount by which the ex-post spend differs from the ex-ante spend -- the property is termed budget balanced up to one project (BB1). With respect to fairness, we take a best-of-both-worlds perspective, seeking outcomes that are both ex-ante and ex-post fair. Towards this goal, we initiate a study of ex-ante fairness properties in PB, including Individual Fair Share (IFS), Unanimous Fair Share (UFS) and their stronger variants, as well as Group Fair Share (GFS). We show several incompatibility results between these ex-ante fairness notions and existing ex-post concepts based on justified representation. One of our main contributions is a randomized algorithm which simultaneously satisfies ex-ante Strong UFS, ex-post full justified representation (FJR) and ex-post BB1 for PB with binary utilities.
Paper Structure (20 sections, 12 theorems, 38 equations, 1 figure, 2 algorithms)

This paper contains 20 sections, 12 theorems, 38 equations, 1 figure, 2 algorithms.

Table of Contents

  1. Introduction
  2. Our Results
  3. Related Work
  4. Preliminaries
  5. Integral Outcomes
  6. Fractional Outcomes
  7. Lotteries and Implementation
  8. Implementing Fractional Outcomes in PB
  9. Handling Hard Constraints
  10. Ex-ante Fairness Concepts
  11. Fractional Random Dictator
  12. BoBW Fairness in PB with Binary Utilities
  13. Impossibility: Ex-ante GFS + Ex-post JR
  14. Ex-ante Strong UFS + Ex-post FJR
  15. The Algorithm: BW-GCR-PB
  16. ...and 5 more sections

Key Result

Theorem 3.2

For any feasible fractional outcome $\vec{p}$, there exists a random process running in polynomial time, that defines random variables $P_i \in \{0, 1\}$ for all $i \in C$ such that the following properties hold:

Figures (1)

  • Figure 1: Summary of best-of-both-worlds fairness results in PB and special cases. Arrows point from generalizations to special cases. Compatibility results are represented by ✓ and impossibility results by ✗. (*) denotes exponential-time results.

Theorems & Definitions (44)

  • Definition 3.1: BB1
  • Theorem 3.2
  • proof
  • proof : Proof of \ref{['enum:marginal-distribution']}
  • proof : Proof of \ref{['enum:degree-preservation']}
  • Definition 3.3: BFx
  • Proposition 3.4
  • proof
  • Definition 4.1: IFS
  • Definition 4.2: Strong IFS
  • ...and 34 more