District-Fair Participatory Budgeting

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.

The (Computational) Social Choice Take on Indivisible Participatory Budgeting

“…is is the case in Amsterdam (City of Amsterdam, 2022) for instance, and to some extent in Paris (City of Paris, 2020) 1 . Motivated by this observation Hershkowitz, Kahng, Peters and Procaccia (2021) investigate the effect of the local versus global implementation of PB processes.…”

“…In their study, Hershkowitz, Kahng, Peters and Procaccia (2021) introduce a model of districtbased PB. Each project belongs to a specific district and contributes a fixed additive amount to the welfare of its district.…”

“…Hershkowitz, Kahng, Peters and Procaccia (2021) show that it is computationally hard to maximise social welfare under district fairness constraints. In addition, they show that one can, in polynomial time, find probabilistic outcomes that maximises the global social welfare while being almost district-fair in expectation.…”

“…We just mention them here and refer the reader to Chapter 8 for more details. Hershkowitz, Kahng, Peters and Procaccia (2021) studied welfare maximisation in a model in which projects are grouped into district. Similarly, Jain, Sornat, Talmon and Zehavi (2021) and Patel, Khan and Louis (2021) investigated different social welfare maximisation when projects are grouped in categories.…”

More Effort Towards Multiagent Knapsack

“…Initiated in Brazil in 1989 in the municipality of Porto Alegre [39], PB has become quite popular worldwide [20], including in the United States [34] and Europe [35]. In the last few years, PB has gained considerable attention from computer scientists [6,38,18,5,7,28,27,26,25,32]. We would like to note that Goel et.…”