Quadratic Funding — A Better Way to Fund Public Goods

Blockchain technology is reprogramming the world. It is opening up financial markets, bringing transparency to supply chains, making asset trading more liquid, among other upgrades. The current crypto-ecosystem is a playground for innovation, and one of the most interesting socio-economic experiments currently being conducted is Quadratic Funding (QF).

It is a capital allocation mechanism that empowers a community to demonstrate their preference for a project by amplifying each donation so that a project with a large number of backers will benefit the most.

In this article, we will dissect what quadratic funding is, how this new governance structure functions, the benefits of using this method and we’ll conclude with analysis of some real-life QF examples.

What is Quadratic Funding?

Quadratic Funding is the mathematically optimal way to fund public goods in a democratic community. It amplifies the donations made by a large community over the contributions made by a small group with big pockets.

But what are public goods?

Economics defines a public good as a commodity or service available to all members of society. It must be:

• Non-rivalrous, which means that use by one member does not decrease availability to others
• Non-excludable which means that everyone should be able to access it

There are three other types of goods: private, shared, and club. Let’s look at these classifications with a matrix:

A knowledge resource for public goods

Now that we have understood what QF benefits, let us discuss its practical functioning.

Vitalik Buterin, Zoe Hitzig, and E. Glen Weyl initially outlined QF in a research paper published in 2018. A primer on the concept, how the exact equation evolved can be found in Vitalik’s blogspot. In simple terms, the amount received by the project is the amount donated. An additional amount is matched by the grant pool, which is equal to the square of the sum of the square roots of contributions received minus the actual contribution. So basically, this fundraise happens in two steps:

1. Individuals crowdfund donations toward public goods
2. These individual contributions are matched by funds from a government, private philanthropist, or grants program.

Let us go through an example of quadratic funding:

A deeper dive into Finematic’s QF example shows how the formula works to arrive at the precise values:

1. Individuals contributed capital to projects A, B, and C
2. After the round, for project A, the square root of each contribution was summed and this sum was then squared. Let us call this number, the QF variable
3. A similar process was carried out for projects B and C
4. Now, project A’s share of the pool was calculated as a weighted average its QF variable
5. The capital was distributed to the other projects through the same mathematical model

The above example depicts that projects with a higher number of contributors are matched with a much larger allocation of the matching pool. Let us explore why this is a massive improvement on the current systems for capital allocation.

Benefits of Quadratic Funding

So as categorized and explained above, public goods are open for everyone to use, and usage by one will not impact the availability for others. In this scenario, Quadratic Funding helps prevent “Tragedy of Commons”. Any individual who sees some incentive in using a public good has no way to exclude others from consuming it, resulting in overconsumption, inefficient use of resources, and ultimately resource depletion.

Quadratic funding emphasizes the number of donations rather than the size of the donation itself. Projects that can get more people to donate to them represent public goods that serve a larger public, so the tragedy of the commons problem is more severe, and hence, contributions to them should be multiplied more to compensate. Therefore, projects serving a wider set of people are assumed to be backed by an equally large number of donors, resulting in significantly high donations from the matching pool. It also helps filter out projects which are in favor of wealthy few.

Use Cases

The Vickrey-Clarke-Groves mechanism is one of the earliest known models idealizing quadratic voting. Since then, the Colorado State Legislature has experimented with this voting mechanism and the Taiwanese presidential hackathon was judged through quadratic voting.

One of the most famous crowdfunding platforms, Gitcoin, uses the QF method to raise funds. Gitcoin lets the community build and fund open-web projects. They have supported a diverse array of projects like Uniswap, EPNS, Finematics, Kickback, among others. By backing high-quality projects, Gitcoin has developed a strong community around itself. Ethereum co-founder Vitalik Buterin uses Gitcoin Grants to discover new projects, and Andre Cronje used Gitcoin Grants to fund his project, Yearn Finance.

Gitcoin has provided US$ 19.8mn in funding to thousands of teams

Here is a table depicting the performance of QF Gitcoin Grants — 3, a total of US$ 100k was distributed between 68 teams:

1.EntHub was granted 3.4 times the amount it raised because of the large community backing it.

2. On the other hand, Lighthouse and Gas Station Network raised large amounts of capital but their matching amounts were low because a large part of their donations was sponsored by a small group of people.

3.To highlight the power of communities further, we look at Ether.js and Gas Station Network.

• Ether.js was given US$ 226 more than GSN even when it had fewer donors and had raised just 13% of the amount as compared to GSN.
• A likely explanation for this is that the 68 supporters of Ether.js uniformly donated for the project while there were few people in GSN’s community who donated very large amounts, while the others contributed tiny capital.
• Unfortunately, we do not have the granular data to substantiate this claim. However, we do believe that something along the lines of this donation pattern occurred for these two projects.

Gitcoin Grants recently concluded the 9th round of funding for blockchain projects and US$ 1.38mn was donated by 12k+ contributors to 812 different projects. Gitcoin’s QF is an important socio-economic experiment, because, with the rise of DAOs and unlocking of treasury tokens in the coming quarters, funding of public goods in the blockchain ecosystem will play a crucial role in expanding the space.

We are confident that the community will create more innovative solutions to identify and support the best projects in the Crypto Industry.

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