Quadratic Funding

The core mechanism calculates the matching amount for a project using the formula: Matching ∝ (Σ √contribution)². This squares the sum of the square roots of individual contributions, ensuring that a large number of small donations can unlock a disproportionately large matching pool. For example, 100 donations of $1 each would generate more matching funds than a single $100 donation.

To prevent exploitation and ensure fair distribution, Quadratic Funding rounds often implement protective parameters:

• Cliff: A minimum threshold of unique contributors required before a project becomes eligible for matching funds.
• Matching Cap: A maximum limit on the amount of matching funds any single project can receive, preventing a single popular project from draining the entire pool.

Quadratic Funding operationalizes the concept of plural funding, where the goal is to fund projects based on the breadth of community support rather than the depth of capital from a few. It is designed to surface projects with widespread, modest support that traditional capital allocation (like venture capital) might overlook, effectively measuring the intensity of a community's collective preference.

A critical challenge for Quadratic Funding is Sybil attacks, where a single entity creates many fake identities to manipulate the matching formula. Solutions to ensure Sybil resistance include:

• Proof-of-Personhood verification (e.g., BrightID, Worldcoin).
• Social graph analysis and unique identity attestations.
• Staking or bonding mechanisms to increase the cost of attack.

The mechanism is highly capital-efficient for discovering valuable public goods. A relatively small matching pool can leverage a much larger amount of community signaling, as each small contribution acts as a vote amplified by the matching funds. This creates a powerful price discovery mechanism for projects that generate positive externalities.

The core mechanism calculates a project's matching amount based on the square of the sum of the square roots of contributions. Key components:

• Matching Pool: The central fund to be distributed.
• Capital-constrained Liberal Radicalism: The formal economic model.
• Sybil Resistance: Critical to prevent manipulation via fake identities.
• Pairwise Coordination: The formula inherently rewards projects with broad, decentralized support over those with a few large backers.

Beyond crypto, QF is being piloted for municipal budgeting and community grants. Within Web3, many DAOs (Decentralized Autonomous Organizations) use QF to allocate portions of their treasury, as it aligns with decentralized governance principles. It is a primary tool for community-driven resource allocation.

Effective QF implementation requires solving key challenges:

• Sybil Attacks: Preventing users from creating multiple identities to game the system, often addressed with proof-of-personhood or credit systems.
• Collusion: Deterring coordinated groups from manipulating outcomes.
• Matching Pool Sustainability: Ensuring a reliable source of matching funds.
• Voter Education: Helping participants understand the quadratic mechanism to make informed decisions.

QF amplifies the power of small contributions, making the funding outcome more representative of the collective preference of a community rather than the wealth of a few large donors. A project with 100 supporters giving $1 each can receive more matching funds than a project with one donor giving $10,000, as the matching is based on the number of unique contributors.

The algorithm is derived from economic theory (Vickrey-Clarke-Groves mechanisms) and is provably optimal for funding non-excludable, non-rivalrous public goods. It efficiently allocates capital to projects that generate the greatest total community value, as measured by the aggregate willingness of participants to contribute.

When implemented on a blockchain, every contribution, matching calculation, and fund distribution is recorded on a public ledger. This creates a cryptographically verifiable and auditable process, eliminating opaque grant committees and building trust through algorithmic fairness and on-chain transparency.

By rewarding broad-based support, QF incentivizes project creators to engage a wide audience and demonstrate genuine utility. This fosters grassroots community building, decentralized governance, and a culture of cooperative funding, as seen in ecosystems like Gitcoin Grants and Ethereum's CLR rounds.

The quadratic formula inherently dilutes the influence of large capital. While a donor's impact increases with their contribution, it does so at a decreasing rate (quadratically). This creates a more pluralistic funding landscape where diverse, community-valued projects can compete effectively against those backed solely by concentrated wealth.

A core challenge is Sybil attack prevention, where a single entity creates many fake identities to manipulate the matching formula. Effective QF implementations require robust identity verification or proof-of-personhood systems (e.g., BrightID, Gitcoin Passport) to ensure one-human-one-vote integrity, which is an active area of cryptographic research.

A central fund, often provided by a protocol or philanthropic organization, that amplifies community contributions. The pool is distributed to projects based on a quadratic formula, which prioritizes projects with broad community support (many small donors) over those with concentrated support (few large donors). This mechanism is the financial engine that makes Quadratic Funding effective.

Two primary implementations of Quadratic Funding on Ethereum. Gitcoin Grants is the most well-known platform, running regular funding rounds for open-source software and public goods. clr.fund is a more decentralized, protocol-native implementation that uses minimal trusted components and can be deployed as a public good for any community.

A broader category of funding mechanisms where the allocation of a shared resource (like a treasury) is determined by aggregating the preferences of a community. Quadratic Funding is a specific, mathematically optimized form of plural funding. Other examples include Conviction Voting and Retroactive Public Goods Funding.

The foundational economic theory behind Quadratic Funding. It posits that the optimal subsidy for a public good is proportional to the sum of the square roots of individual contributions. This mathematically solves the pairwise coordination problem, efficiently funding projects that benefit overlapping groups of people.

A critical security requirement for Quadratic Funding. Since the mechanism rewards a high number of unique contributors, it is vulnerable to Sybil attacks where a single entity creates many fake identities to game the matching. Platforms use identity verification (like Gitcoin Passport), proof-of-personhood, or stake-based weighting to mitigate this.

A complementary funding model popularized by Optimism's RetroPGF. Instead of funding based on projected future work (like QF), it rewards projects for proven, past contributions to the ecosystem. This model reduces speculation and funds work that has already demonstrated value, acting as a results-based counterpart to QF's community-signal-based approach.