  Participatory budgeting refers to the practice of allocating public resources
by collecting and aggregating individual preferences. Most existing studies in
this field often assume an additive utility function, where each individual
holds a private utility for each candidate project, and the total utility of a
set of funded projects is simply the sum of the utilities of all projects. We
argue that this assumption does not always hold in reality. For example,
building two playgrounds in the same neighborhood does not necessarily lead to
twice the utility of building a single playground.
  To address this, we extend the existing study by proposing a submodular
participatory budgeting problem, assuming that the utility function of each
individual is a monotone and submodular function over funded projects. We
propose and examine three preference elicitation methods, including
\emph{ranking-by-marginal-values}, \emph{ranking-by-values} and \emph{threshold
approval votes}, and analyze their performances in terms of distortion.
Notably, if the utility function is addicative, our aggregation rule designed
for threshold approval votes achieves a better distortion than the
state-of-the-art approach.
