  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.
