How does quadratic funding work?

The idea

In 2018, Vitalik Buterin, Zoë Hitzig and Glen Weyl proposed a way to fund public goods. Their first draft was titled Liberal Radicalism; the 2020 revision calls the idea Quadratic Finance.^5,6 Gitcoin, which has run crowdfunding rounds since 2019, calls it quadratic funding.^7,2

The problem it tries to fix is underfunding. Private giving tends to produce too little of a public good, because each giver counts only their own benefit.⁶ So the paper's rule pays out more than people give. A project receives "the square of the sum of the square roots of the contributions".⁶

The effect, in the paper's words: "small contributions are heavily subsidized", while large ones are subsidised least.⁶

The formula in three steps

Here is the paper's rule, one step at a time.⁶

1. Take the square root of each gift.⁶
2. Add up the square roots.⁶
3. Square the total. That is what the project receives under the full rule.⁶

The gap between that amount and what donors gave is paid by someone else. In the paper, a tax covers it. In a grant round, it comes from a sponsor's matching pool.^6,2 We call that gap the full match.⁶

When the pool is smaller

Real sponsors have a budget. The paper's answer is a "capital-constrained" version. A project gets a share, α, of the full rule, plus the rest (1 − α) of what its donors gave.³ The sponsor can turn α down until the budget is "not exceeded".³

Take away what the donors gave, and each project's match is simply α times its full match.³ In our example, the full matches add up to $300 + $0 + $100 = $400. If the pool is only $200, then α = 200 ÷ 400 = 0.5. Project A gets $150, B gets $0 and C gets $50.³

Gitcoin's own description is different. It uses each project's squared total as a weight, then scales every match so that the total "equals the size of the matching pool".² Worked through on the example above, B's squared total of 100 is still a weight, so B would get part of the pool, unlike under the paper's rule. That step is our working, not Gitcoin's.^2,3 Real rounds then adjust results for suspected fake donors, so live numbers will not match a textbook sum.²

Why many small gifts win

Projects A and B each raised $100. Under the paper's rule, A got a full match of $300 from four donors; B got nothing from one.⁶ That is the point. Gitcoin describes quadratic funding as sharing the pool by "how many individual contributors they attract, not just how much money each contributor gives".²

Gitcoin lists the limits too. Projects with an existing audience tend to attract more donors. And people with more money can still gain influence by spreading many gifts around.²

Fake donors: Sybil attacks

If counting people pays, faking people pays too. Gitcoin says quadratic funding "creates incentives to fabricate identities".² Posing as many people is called a Sybil attack. The paper calls it fraud: "when a single citizen misrepresents herself as many".^3,4

The paper is blunt about it. Unchecked, fraud is "a sure arbitrage opportunity" that could turn the system into a way of "lining the pockets of the fraudster".³ It calls identity checks the simplest and most clearly needed defence.³ It also warns about collusion, where groups coordinate their giving.^1,3

How Gitcoin says it defends rounds

Gitcoin's main tool has been a "passport". Donors collect "stamps" from things like social accounts, on-chain history and ID checks. Each stamp adds to a score that decides whether, and how much, a donor's gift counts for matching.⁴

The tool is now called Human Passport. Its maker says it was previously known as Gitcoin Passport, and that quadratic funding only works "if each contribution comes from a unique human".⁸ In its own app, the default passing score is 20 (as of March 2026).⁸

Gitcoin also checks results before paying. It says paying out "tends to take a few weeks so we can check all donations for Sybil interference".⁹ Its page lists other methods that "may reduce, reallocate, or otherwise adjust final allocations".²

No paying for donations

Gitcoin bans buying support. Under its quid pro quo policy, a project may not reward donors for giving to it, for example by refunding their gas fees.¹⁰ Things aimed at every donor in the round are allowed: a general thank-you, an open invitation to a community event, or a badge for taking part. Breaking the rule can get a project removed from the matching.¹⁰