  In participatory budgeting we are given a set of projects---each with a cost,
an available budget, and a set of voters who in some form express their
preferences over the projects. The goal is to select---based on voter
preferences---a subset of projects whose total cost does not exceed the budget.
We propose several aggregation methods based on the idea of cumulative votes,
e.g., for the setting when each voter is given one coin and she specifies how
this coin should be split among the projects. We compare our aggregation
methods based on (1) axiomatic properties, and (2) computer simulations. We
identify one method, Minimal Transfers over Costs, that demonstrates
particularly desirable behavior. In particular, it significantly improves on
existing methods, satisfies a strong notion of proportionality, and, thus, is
promising to be used in practice.
