  We study a mechanism design problem where a community of agents wishes to
fund public projects via voluntary monetary contributions by the community
members. This serves as a model for public expenditure without an exogenously
available budget, such as participatory budgeting or voluntary tax programs, as
well as donor coordination when interpreting charities as public projects and
donations as contributions. Our aim is to identify a mutually beneficial
distribution of the individual contributions. In the preference aggregation
problem that we study, agents report linear utility functions over projects
together with the amount of their contributions, and the mechanism determines a
socially optimal distribution of the money. We identify a specific mechanism --
the Nash product rule -- which picks the distribution that maximizes the
product of the agents' utilities. This rule is Pareto efficient, and we prove
that it satisfies attractive incentive properties: it spends each agent's
contribution only on projects the agent finds acceptable, and agents are
strongly incentivized to participate.
