Optimal Allocation of Limited Funds in Quadratic Funding

We examine the allocation of a limited pool of matching funds to public good projects using Quadratic Funding. In particular, we consider a variation of the Capital Constrained Quadratic Funding (CQF) mechanism proposed by Buterin, Hitzig and Weyl (2019) where only funds in the matching pool are distributed among projects. We show that this mechanism achieves a socially optimal allocation of limited funds.