Participatory budgeting engages the public in the process of allocating public money to different types of projects. PB designs differ in how voters are asked to express their preferences over candidate projects and how these preferences are aggregated to determine which projects to fund. This paper studies two fundamental questions in PB design. Which voting format and aggregation method to use, and how to evaluate the outcomes of these design decisions? We conduct an extensive empirical study in which 1 800 participants vote in four participatory budgeting elections in a controlled setting to evaluate the practical effects of the choice of voting format and aggregation rule. We find that k-approval leads to the best user experience. With respect to the aggregation rule, greedy aggregation leads to outcomes that are highly sensitive to the input format used and the fraction of the population that participates. The method of equal shares, in contrast, leads to outcomes that are not sensitive to the type of voting format used, and these outcomes are remarkably stable even when the majority of the population does not participate in the election. These results carry valuable insights for PB practitioners and social choice researchers.

翻译：参与式预算让公众参与公共资金在不同类型项目间的分配过程。不同的参与式预算设计在如何让选民表达对候选项目的偏好，以及如何聚合这些偏好以确定资助哪些项目上存在差异。本文研究参与式预算设计中的两个基本问题：采用哪种投票格式和聚合方法，以及如何评估这些设计决策的结果？我们进行了一项大规模的实证研究，让1800名参与者在受控环境下参与四次参与式预算选举，以评估投票格式和聚合规则选择的实际效果。我们发现，k-approval方法能带来最佳用户体验。关于聚合规则，贪婪聚合产生的结果对所采用的输入格式和参与人口比例高度敏感。相比之下，均等分配法产生的结果对所采用的投票格式类型不敏感，并且在大多数人口不参与选举时，这些结果也异常稳定。这些结果为参与式预算实践者和社交选择研究者提供了宝贵的见解。