Funding Public Projects: A Case for the Nash Product Rule

TL;DR

This paper introduces a mechanism for funding public projects through voluntary contributions, using the Nash product rule to achieve a Pareto efficient and incentive-compatible distribution of resources among agents.

Contribution

It proposes the Nash product rule as a novel mechanism for allocating contributions in public project funding, ensuring efficiency and incentivizing participation.

Findings

The Nash product rule maximizes the product of agents' utilities.

The mechanism is Pareto efficient.

Agents are strongly incentivized to participate.

Abstract

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.