Quadratic Voting
Quadratic voting is a governance mechanism where the cost of additional votes on an issue increases quadratically, balancing minority and majority interests.
Key Takeaways
- Quadratic voting lets participants express preference intensity: casting N votes on a single issue costs N-squared credits, so concentrating influence on one issue becomes progressively more expensive. This prevents any single voter from dominating outcomes the way token-weighted voting allows.
- The mechanism only works with reliable identity verification: without proof-of-personhood, a whale can split tokens across many wallets to bypass the quadratic cost curve, making Sybil attacks the primary threat to any quadratic voting deployment.
- Quadratic funding (the related capital allocation variant) has seen wider real-world adoption than quadratic voting itself: Gitcoin Grants has distributed over $60 million using quadratic matching to fund public goods across the Ethereum ecosystem.
What Is Quadratic Voting?
Quadratic voting (QV) is a collective decision-making mechanism that allows voters to express not just which option they prefer, but how strongly they prefer it. Each participant receives an equal budget of "voice credits" and allocates them across issues or proposals. The key innovation: the number of counted votes equals the square root of the credits spent, meaning the cost of votes follows a quadratic function.
The concept was first proposed by economist E. Glen Weyl in 2012 and later developed with Eric A. Posner in their 2018 book Radical Markets: Uprooting Capitalism and Democracy for a Just Society. The theoretical foundation draws from the Vickrey-Clarke-Groves (VCG) mechanism for eliciting truthful preferences, adapted specifically for democratic decision-making and on-chain governance.
Traditional one-person-one-vote systems treat every voter's preference as equally intense. A person who is passively indifferent about an issue has the same power as someone whose livelihood depends on it. Token-weighted voting (one token, one vote) swings the other direction, giving all power to the largest holders. Quadratic voting occupies a middle ground: it lets strongly affected minorities concentrate their voice while preventing plutocratic domination.
How It Works
The core rule is simple: casting N votes on a single issue costs N² (N-squared) credits.
| Votes Cast | Credits Spent | Marginal Cost of Next Vote |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 3 |
| 3 | 9 | 5 |
| 4 | 16 | 7 |
| 5 | 25 | 9 |
| 10 | 100 | 19 |
Every voter receives an equal budget of voice credits. In Colorado's state legislature deployment, for example, lawmakers each received 100 virtual tokens. Credits spent on one issue cannot be used on others, forcing voters to prioritize.
The Cost Curve
The marginal cost of each additional vote rises linearly: the Nth vote costs 2N − 1 credits. This progressive cost structure is what captures preference intensity. Spending 9 credits on a single issue (3 votes) signals much stronger preference than spending 1 credit on each of 9 different issues (9 votes spread across issues, each counting as 1).
// Quadratic voting cost function
function voteCost(numVotes: number): number {
return numVotes * numVotes;
}
// Given a credit budget, how many votes can you cast?
function maxVotes(credits: number): number {
return Math.floor(Math.sqrt(credits));
}
// Example: 100 credits budget
// All on one issue: 10 votes (cost: 100)
// Split across 4 issues: 5 + 3 + 1 + 1 = 10 votes
// (costs: 25 + 9 + 1 + 1 = 36 credits, with 64 remaining)Compare this to linear (token-weighted) voting: buying 100 votes costs 100 tokens, and buying 10,000 votes costs 10,000 tokens. Under quadratic voting, 100 votes would cost 10,000 credits, making large-scale influence accumulation prohibitively expensive.
Comparison with Other Governance Models
Quadratic voting is one of several governance mechanisms used in DAO governance. Each makes different tradeoffs:
| Mechanism | Voting Power Formula | Strength | Weakness |
|---|---|---|---|
| Token-Weighted (1:1) | Power = tokens held | Sybil-resistant, simple | Plutocratic: whales dominate |
| Quadratic Voting | Power = √credits spent | Captures preference intensity | Requires Sybil resistance |
| Conviction Voting | Power = tokens × time staked | Prevents vote ambushes | Slow, favors patient capital |
| Vote Escrow | Power = tokens × lock duration | Aligns long-term incentives | Illiquid, rewards lock-up |
Holographic consensus, pioneered by DAOstack, takes a different approach entirely: it attaches a prediction market to each proposal, allowing predictors to "boost" proposals they believe will pass. Boosted proposals switch from requiring an absolute quorum to needing only a relative majority, addressing the scalability problem that plagues DAOs with hundreds of active proposals.
Use Cases
Gitcoin Grants and Quadratic Funding
The most successful deployment of quadratic principles is Gitcoin Grants, which uses quadratic funding (QF) rather than quadratic voting. QF applies the same square-root logic to capital allocation: the matching amount a project receives is proportional to the square of the sum of the square roots of individual contributions.
The practical effect: many small donations generate far more matching than a few large ones. If 100 people each contribute $1 to a project, the matched amount vastly exceeds what a single $100 donation would generate. This incentivizes projects to build broad community support rather than courting a handful of wealthy donors.
Gitcoin Grants has distributed over $60 million to more than 3,700 projects across open-source software, DeFi infrastructure, and community initiatives since its launch. The mechanism was formalized in the 2018 paper "Liberal Radicalism" by Vitalik Buterin, Zoe Hitzig, and E. Glen Weyl, and has become the most widely deployed democratic capital allocation mechanism in the Ethereum ecosystem.
DAO Governance
Approximately 15 major DAOs have adopted quadratic voting in some form, as part of the broader evolution of DAO treasury governance. Notable examples include:
- Gitcoin DAO uses QV and QF as its core governance mechanism for allocating funding across grant rounds
- Optimism Collective used quadratic voting in its first RetroPGF round to allocate retroactive public goods funding, with the program collectively distributing over $100 million
- Element Finance combines quadratic voting for discrete governance decisions with conviction-based mechanisms for ongoing resource allocation
DAOs that have switched from token-weighted voting to quadratic or delegated models have reported voter turnout increasing from roughly 2.8% to 11.4% on average, with proposal quality scores rising approximately 34%.
Government and Civic Use
The Colorado state legislature ran the most prominent government deployment of quadratic voting from 2019 to 2023. The Democratic Caucus of the Colorado State House first used QV in spring 2019 to prioritize 107 spending bills, with each lawmaker receiving 100 virtual tokens. The collaboration with the RadicalxChange Foundation produced a notable result: no representative spent all 100 tokens on a single bill, demonstrating that the trade-off incentive worked as designed.
By 2022, the experiment expanded to bipartisan participation, with the Republican Caucus of the Senate joining. However, a Denver judge ruled in January 2024 that the QV polls violated Colorado's open-meetings law due to their secret-ballot nature, halting the practice.
Other civic deployments have included Taiwan's presidential hackathon, Volt Germany's 2019 party congress for ranking manifesto topics, and Gramado, Brazil's city council for budget prioritization.
The Sybil Attack Problem
The critical vulnerability of quadratic voting in pseudonymous environments like blockchains is the Sybil attack. Because QV's cost curve penalizes concentrating votes in a single identity, splitting tokens across multiple wallets directly undermines the mechanism.
Consider: a voter with 100 tokens in one wallet gets 10 votes (√100). By splitting those same 100 tokens across 100 wallets (1 token each), they cast 100 votes (1 from each wallet). That is 10x the influence for the same token holdings.
// Sybil attack advantage calculation
function sybilAdvantage(tokens: number, wallets: number): number {
const honestVotes = Math.sqrt(tokens);
const tokensPerWallet = tokens / wallets;
const sybilVotes = wallets * Math.sqrt(tokensPerWallet);
return sybilVotes / honestVotes;
}
// Examples:
// 100 tokens, 100 wallets: 10x advantage
// 10000 tokens, 100 wallets: 10x advantage
// The advantage = √(number of wallets)A June 2025 paper published via Circle Research titled "Concave is the New Linear" proved that all wallet-based concave voting mechanisms (including QV) are fundamentally plutocratic when Sybil attacks are possible. The key finding: splitting tokens into equal-size wallets is the optimal attack strategy, and all concave systems collapse to effective one-token-one-vote under Sybil conditions.
Mitigation Approaches
Because quadratic voting depends on one-person-one-budget enforcement, identity verification is essential for any deployment:
- Gitcoin Passport aggregates identity attestations from web2 and web3 sources (GitHub, Twitter, ENS, biometrics), requiring a minimum score to be considered verifiably human
- World ID uses biometrics-based proof of personhood, allowing verified humans to obtain voice credits
- Government ID verification works in civic contexts like Colorado's legislature but does not translate to permissionless blockchain environments
- NFT badges and soulbound tokens can serve as identity anchors tying influence to real contributions rather than disposable addresses
Risks and Considerations
Sybil Resistance Remains Unsolved
No current proof-of-personhood system fully solves the Sybil problem at scale. Biometric approaches raise privacy concerns, social attestation systems can be gamed through collusion, and government ID verification excludes participants in permissionless systems. Until robust identity layers mature, quadratic voting on public blockchains remains vulnerable to the very plutocratic capture it was designed to prevent.
Collusion and Vote Buying
Even with perfect identity verification, voters can collude off-chain to coordinate their credit allocations. A group that agrees to all concentrate credits on the same issue effectively bypasses the individual cost curve. Mechanisms like MACI (Minimum Anti-Collusion Infrastructure) use encryption to make it impossible for voters to prove how they voted, reducing the ability to enforce collusion agreements.
Complexity and Voter Comprehension
Quadratic voting is more complex than simple yes/no or one-token-one-vote systems. Voters must understand the cost curve, make strategic allocation decisions across multiple issues, and reason about marginal costs. In Colorado's deployment, lawmakers adapted well, but broader public adoption may face comprehension barriers.
Legal and Regulatory Uncertainty
Colorado's QV experiment was halted by a judge over open-meetings law violations. The secret-ballot nature of QV raised transparency concerns in public governance contexts. For DAOs and on-chain governance, the off-chain coordination required for identity verification can create tension with decentralization principles.
Quadratic Funding vs. Quadratic Voting
In practice, quadratic funding has seen far wider adoption than quadratic voting for governance decisions. QF's application to capital allocation (matching donations) has proven more tractable than QV's application to collective decision-making, partly because QF operates with real money (making Sybil attacks costly) while QV often uses free voice credits (making Sybil attacks free). Projects evaluating quadratic mechanisms should consider whether QF might better suit their needs than QV.
This glossary entry is for informational purposes only and does not constitute financial or investment advice. Always do your own research before using any protocol or technology.