Public Good Provision in a Large Economy

We propose a new approach to the normative analysis of public-good provision in an economy that is large so that any one individual is too insignificant to have a noticeable effect on the provision levels of public goods. In such an economy, the standard mechanism design problem of calibrating people's payments to the influence they have on public-good provision is moot. In the absence of participation constraints, the first-best provision rule of providing the public good if and only if the average per capita valuation exceeds the per capita cost can be implemented if the costs are shared equally among individuals. Equal cost sharing is actually necessary if the mechanism is to be robust in the sense of Bergemann and Morris (2005). However, the first-best provision rule with equal cost sharing is vulnerable to collective deviations in the sense of Laffont and Martimort (2000). Thus, people with valuations below the per capita provision cost would all benefit from a collective deviation inducing a downward bias into the assessment of the average per capita valuation. We develop a concept of coalition-proofness and show that a coalition-proof and robust mechanism cannot condition on the average per capita valuation, but only on the population shares of people with valuations above and below the per capita provision costs. The result suggests an intriguing link between mechanism design theory for large economies and voting.