Quadratic Voting: Definition, Mechanism and DAO Applications

Definition

Quadratic voting (QV) is a governance mechanism in which the cost of casting multiple votes on a single proposal increases quadratically with the number of votes cast. Under a standard QV system, each participant receives a budget of “voice credits.” The cost of casting N votes on a given issue is N² voice credits. This structure means that the marginal cost of each additional vote rises steeply — expressing a strong preference is possible but expensive.

The quadratic cost function was formalised by economists E. Glen Weyl and Eric Posner in their book Radical Markets (2018), building on earlier theoretical work in mechanism design. The core insight is that a purely one-vote-per-person system fails to capture the intensity of preferences — a voter who cares intensely about one issue cannot signal that intensity. Conversely, a purely money-weighted system (one dollar, one vote) allows wealthy participants to completely dominate outcomes. Quadratic voting attempts to occupy a middle ground: intensity of preference can be expressed, but the cost of doing so increases rapidly, limiting the ability of any single participant to dominate through sheer resource accumulation.

The Mathematical Foundation

The quadratic cost function can be expressed simply:

If a participant wishes to cast N votes on an issue, the cost in voice credits is N².

• 1 vote costs 1 credit
• 2 votes cost 4 credits
• 3 votes cost 9 credits
• 4 votes cost 16 credits
• 10 votes cost 100 credits

A participant with 100 voice credits can cast 10 votes on a single issue, or they can distribute their voice across multiple issues — casting 1 vote on 100 issues, 2 votes on 25 issues, or any other combination. The quadratic cost structure means that concentrating voice on a single issue is increasingly expensive relative to spreading it across multiple issues.

The result, in theory, is a governance system where aggregate outcomes reflect the weighted sum of individual preference intensities rather than the raw wealth of participants. A large number of moderately interested parties can outweigh a small number of highly interested parties if the former collectively care more in aggregate — which is the intended democratic property.

How Quadratic Voting Addresses Plutocracy

In a standard token-weighted voting system (one token, one vote), a participant with one million tokens has exactly one million times the governance influence of a participant with one token. Governance outcomes will tend to reflect the preferences of the wealthiest token holders regardless of the breadth or intensity of preference in the broader community.

Quadratic voting disrupts this linearity. Under QV, a participant with one million voice credits can cast one thousand votes on a single issue (since 1000² = 1,000,000). A participant with one credit can cast one vote. The ratio of influence is therefore 1,000:1 — significantly less than the 1,000,000:1 ratio in a linear token-weighted system. The square root compression of the cost function is what reduces (but does not eliminate) the influence advantage of wealthy participants.

Critically, QV also preserves intensity expression. Under a one-person-one-vote system, every participant has equal influence regardless of how much they care about the issue. QV allows a participant who cares very strongly about one particular question — and is willing to spend the majority of their voice credit budget expressing that preference — to do so, while still remaining constrained by their total budget.

The Sybil Resistance Problem

Quadratic voting’s mathematical elegance depends critically on one assumption: that each participant receives their voice credit budget once, as an individual, and cannot obtain more by creating additional identities. If a participant can create ten pseudonymous identities — each receiving its own voice credit budget — they can deploy ten times the voice on any given proposal, effectively recreating the plutocracy problem through identity multiplication rather than wealth concentration.

This vulnerability is called a Sybil attack, named after the 1973 psychological case study of a woman with multiple personalities. A Sybil attack on a QV system involves creating large numbers of fake identities to multiply voting power without limit. In a pseudonymous blockchain environment, where address creation is costless and identity verification is not natively available, Sybil resistance is an unsolved technical problem.

Without a reliable one-person-one-address guarantee, quadratic voting’s anti-plutocracy properties are entirely nullified. This is why QV has not been adopted at scale in major DeFi governance systems, despite theoretical interest and genuine enthusiasm from governance researchers. The protocols that would benefit most from QV — large DeFi protocols with millions of token holders distributed globally — are precisely the systems where Sybil resistance is hardest to guarantee.

Attempts at Sybil-Resistant Identity

Several projects have attempted to build infrastructure that would enable quadratic voting by providing credible proof of unique personhood.

Gitcoin Passport is a reputation-aggregation system that collects verifiable credentials from multiple sources — social platforms, government-adjacent identity systems, biometric providers — to produce a composite “humanity score.” Gitcoin uses this score to weight quadratic funding rounds, with higher-trust passports receiving greater influence. This approach is pragmatic but imperfect: a determined Sybil attacker can accumulate credentials across multiple identities, and the verification methods exclude participants without access to the required platforms.

Worldcoin (now World) uses iris biometrics captured by a physical “Orb” device to produce a zero-knowledge proof of unique personhood. The protocol claims to enable one-person-one-wallet proof without revealing the underlying biometric data. If deployed at meaningful scale, Worldcoin’s proof-of-personhood could in principle enable on-chain quadratic voting. The ethical, privacy, and adoption questions around collecting iris scans from global populations remain deeply contested.

Proof of Humanity uses video verification and social vouching to establish unique personhood claims on-chain. The protocol creates a registry of verified humans that could serve as the eligibility list for a QV system. Scale and geographic coverage remain limiting factors.

None of these approaches has achieved the scale, reliability, and trust required to underpin governance of major DeFi protocols with hundreds of millions of dollars at stake. Sybil resistance remains the principal barrier to practical QV adoption.

Quadratic Funding: Gitcoin Grants

The most prominent real-world application of quadratic principles to DAO-adjacent resource allocation is not quadratic voting but the closely related mechanism of quadratic funding, implemented by Gitcoin Grants.

Quadratic funding (QF) applies the quadratic principle to public goods grant allocation rather than governance voting. In a QF round, individual contributors allocate small amounts to projects they wish to support. The matching pool — typically held by a protocol or foundation — distributes matching funds according to a formula that amplifies the number of contributors rather than the total amount contributed. A project that receives $10 donations from 100 people receives substantially more matching than a project that receives a $1,000 donation from a single contributor.

Gitcoin has deployed quadratic funding across dozens of grant rounds for Ethereum ecosystem public goods, allocating tens of millions of dollars in a manner that is demonstrably more responsive to broad community support than a simple grant committee process. Gitcoin Grants represents the most mature and most impactful application of quadratic mechanism design in the Web3 ecosystem.

Comparison with Alternative Governance Mechanisms

One-token-one-vote is simpler, requires no identity infrastructure, and is compatible with pseudonymous participation. Its weakness is explicit plutocracy — governance outcomes reflect the preferences of the wealthiest holders.

Conviction voting addresses temporal gaming (short-term vote accumulation) by requiring sustained signal over time, but does not address the wealth concentration problem inherent in token-weighted systems.

Reputation-based voting assigns governance weight based on demonstrated contribution or expertise rather than token holdings. This avoids plutocracy but introduces subjective judgements about who deserves reputation, and creates its own capture risks.

Quadratic voting theoretically addresses plutocracy while preserving preference intensity expression, but requires Sybil resistance that is not currently available at scale in pseudonymous blockchain environments.

Swiss Context

Switzerland has been a significant centre for governance mechanism research, with the ETH Zurich and the University of Zurich both active in mechanism design and decentralised governance studies. Swiss-domiciled protocol foundations — including Web3 Foundation and the broader Polkadot ecosystem — have shown interest in governance mechanism innovation, with Polkadot’s OpenGov incorporating multiple tracks and adaptive quorum mechanisms that address some of the same problems as QV.

Academic interest in quadratic voting within Switzerland’s research community reflects a broader pattern: the country’s concentration of protocol foundations, cryptography researchers, and governance scholars creates an unusually dense ecosystem for the translation of theoretical governance mechanism design into practical protocol applications. When Sybil resistance is solved at meaningful scale, Swiss-based protocol foundations are likely to be among the first adopters of quadratic governance mechanisms.

Donovan Vanderbilt is a contributing editor at ZUG DAO, a publication of The Vanderbilt Portfolio AG, Zurich. The information presented is for educational purposes and does not constitute investment advice.