Sustainable Quadratic Financing

Applying quadratic funding to real DeFi to better secure loans

Martin Krzywinski’s Circular π Art

Quadratic voting and quadratic funding have been exemplary protocol design primitives that have expanded far beyond Ethereum throughout the EVM multiverse (e.g., Polygon, Optimism, Avalanche, Celo, etc.). Both have the same aim — to more equitably distribute influence (whether based in capital or perspective) based on the volume of supporters rather than undue influence from a select few.

Quadratic voting is oftentimes referenced in the context of protocol governance to minimize the effects of plutocracy, whereas quadratic funding is referenced in the context of funding public goods / initiatives through collecting community sentiment and commitment before matching said commitments. The purpose of this brief is to introduce ‘Quadratic Financing” which uses the quadratic funding model and applies it to the context of decentralized finance and mitigating lending risk (in particular).

If you’re unfamiliar with quadratic voting and/or funding, I encourage you to check out the following articles:

An Introduction to QFi

Introduced by the Umoja protocol. quadratic financing (a.k.a., “QFi”) is quadratic funding applied to decentralized finance (i.e., “DeFi”) protocols that provide collateralized, crowdsourced lending. Specifically, the model is applied to a DeFi protocol that passes three design criteria:

  1. The protocol crowdsources debt financing capital from multiple liquidity providers by using a Lending Pool or Liquidity Pool.
  2. The protocol uses junior tranche LPs (i.e., Liquidity Providers) and/or collateral backers (i.e., those that provide liquidity specifically for collateral provision rather than loan funding provision) that may selectively contribute capital to a specific Borrower.
  3. The protocol uses a Reserve Treasury / Pool of funds that are staked by protocol Stakers (not referred to ‘liquidity providers’ in the context of this brief) to provide default protection to Collateral Backers (as they are one of the first stakeholders directly affected by Borrower default).

QFi’s aim is simple: Distribute pooled loan financing to Borrowers in proportion to the support provided to the Borrower by collateral backers or junior tranche liquidity providers. The term “support” is measured both in the sum total of capital contributed by Borrower-supporting stakeholders as well as the sum total of Borrower supporters itself.

In practice, QFi materializes as follows:

  1. Collateral Backers show their support to a particular Borrower Pool (i.e., loan request) by committing their capital to the pool. The goal of the pool is to crowdsource the loan’s collateral so that it is fully secured.
  2. A matched amount of loan financing, crowdsourced from multiple Liquidity Providers, is provided to each Borrower Pool and is calculated by using the quadratic funding formula where the amount of collateral received by the Borrower Pool (from Collateral Backers) is proportional to the square of the sum of the square roots of collateral contributions received.
  3. The funds collected in the Lending Pool (from Liquidity Providers) are used to magnify the individual collateral contributions of Backers to different Borrower Pools. If the amount of allocated liquidity (from the Lending Pool) is more than the amount of collateral provided by Backers) to the Borrower Pool, then the extra liquidity is automatically staked into a Reserve pool purpose-built to provide default coverage to Collateral Backers to reduce their risk.

The QFi model solves two DeFi problems: (1) Determining how to fairly and intelligently disburse pooled debt financing capital, and (2) Determining how to minimize protocol stakeholder risk so that you may maximize protocol TVL (e.g., More borrowers → More loan requests → More loan financing → More loan collateral → More staking → All equals higher TVL). Figure 1.0 visualizes the QFi Flywheel below:

Sustainable Quadratic Financing Flywheel

The math stays the same — the use case is what’s changed.

An Example of QFi

To understand the concept of quadratic financing better, we can update a commonly referenced example and update the context / protocol design considerations (1).

Quadratic Funding Example (Finematics)

Imagine that we have $10,000 in the protocol’s Lending Pool that was provided by Backers (i.e., collateral providers) and we have 3 borrowing pools attempting to acquire loan financing (2).

  • Borrower Pool A got $1,000 in funding from 5 Backers ($200 each).
  • Borrower Pool B also received $1,000 but from 2 Backers ($500 each).
  • Borrower Pool C received the same amount — $1,000 — from 20 Backers ($50 each).

Matched amounts are calculated by using the quadratic funding formula where the amount received by the project is proportional to the square of the sum of the square roots of Backer contributions received. Borrower Pool A got an additional $1851.85 which is an extra ~185% on top of the contributed collateral amount. This means that Borrower Pool A has $1,000 in collateral and $1,851.85 in loan financing, and thus can receive a $1,000 fully secured loan. The additional amount of financing (i.e., the $851.85) will go toward the protocol’s Reserve Treasury in the form of staked capital to generate Liquidity Providers an additional, low-risk, stable return AND further protect Backers.

Of course, in the real world scenario, a Borrower Pool would most likely receive multiple different contributions with different amounts, for example, $1, $5, $20 etc, but the principle stays the same — more collateral contributions = higher the matched loan financing.


Though quadratic financing is yet another use case under the quadratic funding umbrella, it demonstrates how protocol design and game-theory inspired formulaic primitives can be reorganized to find amazing ways to advance decentralized financial services. In this case, QFi can facilitate simple loan financing distribution in direct proportion to the sentiment and collateral of Backers that conduct due diligence on Borrowers while also helping protect said Backers from their risk of Borrower default. It’s mechanisms like these — derivative cryptoeconomic design primitives — that will be essential for Real DeFi (DeFi that supports normal consumers and businesses by attending to traditional market needs) to scale.



CEO of Umoja Labs, Former Head of ConsenSys Social Impact, @Goldman Alum, @Cisco Alum, @TFA Alum, Activist, Intense Autodidact

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Robert Greenfield IV

CEO of Umoja Labs, Former Head of ConsenSys Social Impact, @Goldman Alum, @Cisco Alum, @TFA Alum, Activist, Intense Autodidact