  Participatory budgeting (PB) is a democratic process where citizens jointly
decide on how to allocate public funds to indivisible projects. This paper
focuses on PB processes where citizens may give additional money to projects
they want to see funded. We introduce a formal framework for this kind of PB
with donations. Our framework also allows for diversity constraints, meaning
that each project belongs to one or more types, and there are lower and upper
bounds on the number of projects of the same type that can be funded. We
propose three general classes of methods for aggregating the citizens'
preferences in the presence of donations and analyze their axiomatic
properties. Furthermore, we investigate the computational complexity of
determining the outcome of a PB process with donations and of finding a
citizen's optimal donation strategy.
