Participatory budgeting with cumulative votes

In participatory budgeting a group of decision makers is given a set of projects-each with a cost-and has to decide which projects should be funded within the constraints of an available budget. Each decision maker, in some form, expresses their preference over the projects. The goal of an aggregation procedure is to select-based on voter preferences-a subset of projects whose total cost does not exceed the budget and optimal in some sense. We propose several aggregation methods based on the idea of cumulative votes, e.g., for the setting when each of the n voters is given one coin equal to [Formula: see text]th of the budget 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 class of methods, Minimal Transfers, that demonstrates particularly desirable behaviour. In particular, it satisfies a strong notion of proportionality, and, thus, is promising for its use in practice.