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What is Quadratic Funding (QF)?

Last modified: December 2, 2020
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Quadratic Funding (QF) is a precise formula for allocating a central matching fund optimally and democratically. 

Matching funds are widely used by communities to make better decisions about how to collectively fund their common resources, which are often called public goods. Traditional matching schemes promise to match individual contributions at a certain rate, such as 1:1, and up to a certain amount, such as $100. 

Although their constraints are arbitrary, matching funds help address two problems. First, central funders like political institutions and philanthropists suffer from an “information” problem, in that they do not know how much to support a certain good. Matching funds allow them to harness decentralized information from the community about what should be funded. Second, individuals, often a small part of a large group, have incentives to “free ride” and contribute less than is optimal to a public good. Matching funds offer small voices an incentive to contribute as much as large voices who usually dominate these decisions.

QF builds off this democratic character by proposing a systematic, optimal mechanism for matching funds. Smaller contributions receive larger matches. Contributions to widely-beneficial resources, those with many other contributions already, receive larger matches. And small minorities still benefit from smaller matches.  

This new approach to political economy bridges the usual divide between the economy and politics, bringing political values of equality and cooperation into the economy, and agency and flexible choice into political life. With QF our commitments to different issues and communities can shift more gradually, rather than a sharp binary between voice and exit. 

In our newly interconnected and interdependent world, most of our actions, such as producing new research, open-source software, or high-quality journalism, bring value to many others and are primary sources of innovation and wealth creation. But both markets and governments struggle to quantify the value of such actions; we often refer to this problem as a “tragedy of the commons.”  GCRI aims to overcome this using QF, a new way of measuring social value

How does this work exactly?

It is critical to engage every member of our community and let them be active participants in productive discourse and deliberation.  QF is a large-scale preference expression tool that will allow our stakeholders to make more informed and democratic group decisions. Unlike ever before, we can elicit informed and rich feedback about a community’s true needs and priorities.

Step 1—Project proposal phase

Participants can submit proposals and vote on one another’s proposals (via Quadratic Voting) in an online system. This stage of the process would mirror the government of Taiwan’s Presidential Hackathon

[Internal note: Recommendations for GCRI at this stage: (1) to go through the list of leading vote-getters to ensure legitimacy and compatibility (e.g., we should not allow QF to operate on both “expand the dam” and “close the dam” options), and (2) to create separate categories for proposals.]

Step 2—QF funding round

Participants can contribute directly to the projects they care about and, according to the formula, the projects with wider bases of support receive larger matches. 

In technical terms, total funding for a project is the square roots of each contribution, summed up, and then squared.  The difference between the total funding and the sum of the individual contributions is made up by GCRI’s central matching fund. Play around with the math here.

GCRI plans to schedule funding rounds at regular intervals (e.g., every month or quarter). At the end of the round, matches are disbursed to projects.  This step ensures that projects must have repeated, widespread support to continue unlocking large matches. 


Why is this “optimal”?

The innovation is in accounting for the tragedy of the commons: each contribution to a project gets multiplied, or subsidized, by the total number of people who contribute (N) because the benefit of every contribution is spread across all N contributors. [To understand this point more clearly, read the example of Alice and Bob here.] The result is that the project receives the square of the sum of the square roots of all contributions to it. One implication of this rule is that, as the number of contributions increases, the amount of funding grows as the square of this number. With QF, we can more precisely understand how much members of the community benefit from different projects.


Protections Against Fraud and Collusion

GCRI recognizes and will take steps to address certain challenges with QF.

One challenge is that the effectiveness of QF can be undermined when one person pretends to be many, or when groups of people collude. QF requires a model of identity where individuals cannot easily pretend to be multiple people. Otherwise, they can always evade the quadratic costs of greater influence on a collective decision, and the mechanism collapses into linear vote-buying. To address fraud, security measures could include SMS and Twitter verification.

To address collusion, we recommend requiring contributors to certify that they are not acting on anyone else’s behalf. Further measures may include reducing the size of a match when the group supporting a given cause shares characteristics that make them likelier to be colluding, such as being members of the same family or having many social connections. These modifications are not necessary at first but maybe useful eventually. 

To prevent people from selling their votes (bribery), votes should be cast anonymously and privately, so that even the person who made the vote can’t prove to anyone else what they voted for. This is the same logic as secret ballots on regular election days.

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