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.

翻译：参与性预算编制是市政府选择公共项目以居民投票为基础筹资的一种方法。许多城市在地区一级使用参与性预算编制方法。通常,预算按其人口比例在地区之间分配,每个地区对地方项目进行选举,然后用预算为选民最喜欢的项目提供资金。然而,地区一级的参与性预算编制可以产生不良的社会福利,因为它不一定为跨地区支持的项目提供资金。另一方面,只考虑全球社会福利的决策可能对地区不公平:社会福利最大化解决方案可能不会为一个地区喜欢的任何项目提供资金,尽管其选民向城市缴纳税款。因此,我们研究如何在单一的全市选举的参与性预算编制环境中公平地尽量扩大社会福利,我们提出公平的概念,保证每个地区至少能像在地区一级选举中那样得到多少福利。我们表明,尽管按照这种公平概念优化社会福利是硬的,但我们可以有效地为福利-最佳结果建造彩票,而福利-最佳结果则是公平的。此外,当我们被允许过公平的预算宽松时,我们可以稍有限度地表现出公平性。