Quadratic Funding

Funding by Number of Supporters, Not Size of Wallet

Quadratic funding (QF) is a mechanism for allocating a shared matching pool to public goods — open-source software, community projects, research — in a way that reflects how many people support something, not just how much money a few big donors give. Contributors make small donations to projects they value, and a matching pool tops those up using a formula that gives far more weight to the number of contributors than to the size of contributions. A project that many people each give a little to can receive more matching than one a single whale funds heavily. Gitcoin popularised QF for funding Ethereum public goods.

Why This Is Clever

Ordinary funding is plutocratic: whoever has the most money decides what gets funded. QF is designed to be more democratic — it optimises for broad community support, so a project loved by a thousand ordinary people beats one bankrolled by a single rich backer. It tries to fund what a community actually collectively wants, using the matching pool to amplify grassroots preferences. This makes it a promising tool for funding public goods, which markets chronically underfund because their benefits are shared and hard to monetise.

• QF allocates a matching pool to public goods by breadth of support
• The formula weights the number of contributors far above the size of contributions
• Many small donors can out-match a single large one
• Gitcoin popularised it for funding Ethereum/open-source public goods

The Math, Intuitively

The core of QF is that a project's matched amount is based on the square of the sum of the square roots of individual contributions. The practical effect: take each contribution, square-root it, add those up, then square the total. Because square roots dampen large amounts and reward many separate contributions, the formula strongly favours breadth. Ten people giving one dollar each produce a much larger matched amount than one person giving ten dollars, even though the raw total is the same. Under idealised assumptions, QF is proven to allocate the matching pool in proportion to the true collective value the community places on each public good — a genuinely elegant result.

The Sybil Problem

QF's strength — rewarding many distinct contributors — is also its fatal weakness if identities are not real. Because more unique contributors means dramatically more matching, an attacker who creates many fake identities (a sybil attack) and has each 'person' donate a small amount can capture a large share of the matching pool illegitimately. This is not a corner case; it is the central practical threat to QF, and every real deployment lives or dies by its sybil resistance. Without robust proof that contributors are distinct humans, QF degrades into a mechanism for whoever can fake the most identities — the opposite of its democratic intent.

Defending With Identity and Collusion Resistance

Real QF systems bolt on defences. Proof-of-personhood and identity-scoring systems (Gitcoin Passport, for instance) try to weight or filter contributions by how likely each account is a unique human, reducing the payoff of sybils. Collusion resistance is a related concern: groups coordinating to game the pool (or bribing others to donate to their project) undermine the mechanism, motivating research into cryptographic approaches (like MACI — Minimal Anti-Collusion Infrastructure) that hide individual votes to make bribery unenforceable. The honest picture is that QF is powerful in theory but only as good as its identity and anti-collusion layer in practice; the mechanism and its sybil defences are inseparable.

• Matched amount ≈ (sum of square roots of contributions), squared — breadth dominates size
• Under ideal assumptions QF allocates matching in proportion to true collective value
• Sybil attacks (many fake identities giving small amounts) are the central threat
• Proof-of-personhood and anti-collusion (e.g. MACI) are essential, not optional

Constrained QF and Real-World Adjustments

Pure QF assumes unlimited matching and perfect identities; real deployments adjust heavily. Matching pools are finite, so budgets are normalised and capped, which distorts the ideal proportions. Contribution caps, minimum thresholds, per-project matching limits, and pairwise-bounded QF (which limits how much any pair of contributors can jointly influence, blunting collusion) are all used to make QF robust in messy reality. Each adjustment trades some theoretical optimality for practical resistance to gaming. Understanding a specific QF round means reading its rules — the matching cap, the identity requirements, the collusion mitigations — because these determine the actual incentives far more than the textbook formula does.

QF in the Broader Public-Goods Toolkit

Quadratic funding is one instrument in a growing kit of crypto mechanisms for funding shared goods, alongside retroactive public-goods funding (reward proven impact after the fact), conviction voting (continuous preference-weighted allocation), and direct grants. Each suits different situations: QF is good for surfacing broad community preferences among many candidate projects; retroactive funding is better when impact is easier to judge in hindsight than to predict; conviction voting suits ongoing, evolving allocation. Sophisticated ecosystems combine them — for example, QF rounds to fund promising work and retroactive rounds to reward what actually delivered. Seeing QF as one tool with specific strengths and failure modes, rather than a universal solution, is the mature framing.

What Determines Whether QF Works

For a serious observer, a QF program's credibility rests on a few concrete factors: the robustness of its proof-of-personhood (weak identity = sybil capture), the collusion mitigations in place, the size and rules of the matching pool, and the transparency of how contributions and matching are computed and audited. A well-run QF round with strong identity and clear rules can genuinely direct funding toward community-valued public goods that markets would ignore — a real contribution. A poorly-defended round becomes a game of manufactured identities and coordinated donations that funds the best gamers. QF is neither a magic democratiser nor a broken toy; it is a powerful mechanism whose real-world legitimacy is decided by the unglamorous identity-and-rules layer wrapped around the elegant math.