Quadratic funding

The mechanism computes each project's matching by squaring the sum of the square roots of individual contributions, following the formula M = (Σ √cᵢ)². This compresses the influence of large donations and amplifies projects with broad support: a dollar spread across many people counts for more than a dollar from one. The outcome measures collective preference rather than purchasing power.

Quadratic funding applies to fund allocation the same principle as quadratic voting, where cost scales with the square of intensity, and it optimizes funding for public goods the market provides insufficiently. It has known limits: the matching requirement scales quadratically and the pool is finite, so in real rounds it is used up quickly, and it is wise to mitigate collusion and sybil attacks with proof-of-unique-identity.

It was formally proposed in 2018 by Vitalik Buterin, Zoë Hitzig and E. Glen Weyl in the Liberal Radicalism paper. It is the most widely deployed democratic capital-allocation mechanism in the Ethereum ecosystem. Gitcoin Grants is its largest and longest-running deployment, and clr.fund runs privacy-preserving rounds on Ethereum. The theoretical framing connects to RadicalxChange's Plural Funding.