Fair Lotteries for Participatory Budgeting

An interactive demo of the ballot-weighted lottery algorithms from the paper:
Aziz, Lu, Suzuki, Vollen & Walsh — AAAI 2024

Read the Paper Try the Demo

What is Participatory Budgeting?

Participatory budgeting (PB) is a democratic process in which citizens vote on how a public budget should be spent across a set of projects (e.g., a park, a library, road repairs). Each voter approves a subset of projects, and an algorithm selects a feasible subset that fits within the budget.

What do the algorithms do?

Standard PB rules are deterministic — they always pick the same outcome, which may be unfair to minority voters. This paper introduces lottery-based rules that output a probability distribution over feasible outcomes, then use dependent rounding (BB1) to pick a single discrete outcome. Two algorithms are provided:

  • BW-GCR-PB — uses the Greedy Cohesive Rule as its backbone.
    Guarantee: Full Justified Representation (FJR).
    Run Time: Exponential.
  • BW-MES-PB — uses the Method of Equal Shares as its backbone.
    Guarantee: Extended Justified Representation (EJR).
    Run Time: Polinomial.

Both guarantees ensure that every cohesive group of voters gets a fair share of the budget outcome proportional to their size and both also ensure strong UFS property.

How to use the demo

  1. Go to Demo.
  2. Enter a budget, a list of projects with costs, and voter preferences — or click Fill with Random Data.
  3. Choose an algorithm and click Run Algorithm.
  4. See the selected projects, probability vector, and fairness guarantees on the result page.