Onchain Atlas

Quadratic Funding

A way to distribute a shared matching pool so that projects backed by many small donors get matched much more generously than projects backed by one big donor giving the same total.

Also called: QF · matching funds by square-root weighting · democratic matching

What it is

Quadratic funding is a method for allocating a pool of matching funds across public-goods projects based on crowdfunding patterns. Instead of matching donations dollar-for-dollar, it rewards the number of distinct contributors far more than the size of any single contribution — so a project with 100 people each giving $1 gets matched much more heavily than a project that received one $100 donation, even though both raised the same amount directly.

How it works

  1. A round is set up with many eligible projects and one shared matching pool, usually funded by a sponsor, protocol treasury, or donations.
  2. Individual donors contribute any amount they want to any projects they choose during the round.
  3. For each project, the system takes the square root of each individual contribution and sums those square roots, then squares that sum — this "sum of square roots, then squared" calculation is the quadratic part.
  4. Because square-rooting a large number gives proportionally less than square-rooting many small numbers that add to the same total, this formula produces a much higher score for broad-based support (many small donations) than for concentrated support (few large donations) of equal total value.
  5. Each project's calculated score, minus what was actually donated, roughly represents its "ideal" matching amount reflecting the strength of its broad-based demand.
  6. Because the matching pool is limited, every project's ideal match is typically scaled down proportionally so the total payout fits within the available pool.
  7. At the end of the round, the matching pool is distributed according to these scaled amounts, on top of the direct donations each project already received.
  8. Results and calculations are typically published so anyone can verify the payouts.

Why designers use it

  • Surfaces genuine grassroots demand for public goods rather than letting whoever has the deepest pockets decide funding priorities.
  • Lets a sponsor's matching budget go further in expressing collective community preference instead of the sponsor picking winners directly.
  • Encourages projects to build a genuine base of many small supporters rather than courting one wealthy patron.
  • Provides a transparent, formulaic, and auditable way to fund public goods without a central committee making the final call.

Failure modes

  • Sybil attacks: since the formula rewards contributor count over size, an attacker can split themselves into many wallets each donating a small amount to inflate their own project's match — the core exploit target of every QF round.
  • Collusion rings: groups of real people coordinating to donate small amounts to each other's projects can extract disproportionate matching funds without genuine broad public support.
  • Whale-disguised-as-many: a well-funded backer distributing funds across many wallets to donate "small" amounts can mimic organic grassroots support.
  • Pool exhaustion by volume: if far more legitimate demand shows up than the matching pool can support, everyone's payout gets diluted, sometimes making participation feel not worth the effort.
  • Identity verification friction: strong sybil resistance usually requires proof-of-personhood or reputation systems, which add UX friction, cost, or centralization risk to what's otherwise a purely algorithmic mechanism.

What to check before using it

  • Decide what sybil-resistance layer you'll pair with QF (proof of personhood, social graph analysis, stake-based identity) since the formula is only fair if one-person-one-identity roughly holds.
  • Model how collusion detection and result review will work — most real deployments retroactively adjust or flag suspicious donation clusters.
  • Size the matching pool relative to expected donor turnout so payouts remain meaningful rather than diluted to near-zero.
  • Decide on round cadence and eligibility criteria for projects, since QF's fairness properties assume a reasonably open, contestable set of participants.
  • Plan for transparent publication of contribution data and calculations, since the mechanism's legitimacy depends on being independently auditable.

Experiments that used it · 3

Shown oldest first, so you can watch the design evolve.

Gitcoin Quadratic Funding
Gitcoin's Grants Program pioneered real-world quadratic (matching) funding, distributing a shared matching pool to open-source and public-goods projects in proportion to the breadth of their small-donor support.
2019 major success
clr.fund
A permissionless, trust-minimized quadratic funding protocol for Ethereum public goods that used MACI zk-SNARK voting to make contributions bribery-resistant.
2020 partial success
Allo Protocol
Gitcoin's open-source smart-contract framework for programmable onchain capital allocation — pools plus pluggable strategy contracts — that powered Gitcoin Grants rounds before entering maintenance mode after Gitcoin Labs and the Allo.Capital spinout wound down.
2023 technically successful commercially unsuccessful