Discrete public goods under threshold uncertainty

A discrete public good is provided when total contributions exceed the contribution threshold, yet the threshold is often not known with certainty. I show that the relationship between the degree of threshold uncertainty and equilibrium contributions and welfare is not monotonic. For a large class of threshold probability distributions, equilibrium contributions will be higher under increased uncertainty (e.g., a mean-preserving spread) if the public good's value is sufficiently high. Otherwise, and if another condition on the distribution's mode is met, contributions will be lower. The same result also obtains if a single-crossing condition of the pdfs is met.