District-Fair Participatory Budgeting

TL;DR

This paper addresses fair social welfare maximization in city-wide participatory budgeting, proposing a fair lottery approach and a relaxed fairness solution that maximizes welfare despite computational complexity.

Contribution

It introduces a fairness notion ensuring districts receive at least their district-level welfare and provides efficient algorithms for fair lotteries and welfare maximization with slight budget relaxation.

Findings

Efficient construction of fair lotteries over welfare-optimal outcomes.

NP-hardness of welfare maximization under strict fairness constraints.

Relaxed fairness allows for welfare-maximizing solutions that may overspend.

Abstract

Participatory budgeting is a method used by city governments to select public projects to fund based on residents' votes. Many cities use participatory budgeting at a district level. Typically, a budget is divided among districts proportionally to their population, and each district holds an election over local projects and then uses its budget to fund the projects most preferred by its voters. However, district-level participatory budgeting can yield poor social welfare because it does not necessarily fund projects supported across multiple districts. On the other hand, decision making that only takes global social welfare into account can be unfair to districts: A social-welfare-maximizing solution might not fund any of the projects preferred by a district, despite the fact that its constituents pay taxes to the city. Thus, we study how to fairly maximize social welfare in a participatory budgeting setting with a single city-wide election. We propose a notion of fairness that guarantees each district at least as much welfare as it would have received in a district-level election. We show that, although optimizing social welfare subject to this notion of fairness is NP-hard, we can efficiently construct a lottery over welfare-optimal outcomes that is fair in expectation. Moreover, we show that, when we are allowed to slightly relax fairness, we can efficiently compute a fair solution that is welfare-maximizing, but which may overspend the budget.