Quadratic Voting

Quadratic voting (QV) is a system for preference expression in collective decisions in which the cost of casting N votes on an issue equals N². A voter who wants to cast 3 votes on an issue must spend 9 voting credits; casting 5 votes costs 25 credits. This quadratic cost curve allows individuals to express strong preferences on issues they care deeply about while preventing wealthy participants from dominating all decisions with money. Proposed by economist E. Glen Weyl (with extensions for public goods by Vitalik Buterin as “Quadratic Funding”), QV has become influential in DAO and Web3 governance design.


How Quadratic Voting Works

Setup:

  • Each participant receives a fixed budget of voting credits (e.g., 100 credits)
  • They can allocate credits across multiple proposals
  • Voting N times on one proposal costs N² credits

Example with 100 credits:

Votes on Issue A Credits Spent Credits Remaining
1 vote 1 99
3 votes 9 91
5 votes 25 75
7 votes 49 51
10 votes 100 0

Why quadratic?

The marginal cost of each additional vote increases linearly. The 5th vote costs 9 credits (5² – 4² = 25 – 16 = 9). The 10th vote costs 19 credits. This means:

  • Buying a few extra votes on something you care about is cheap
  • Buying 100 votes on one thing costs 10,000 credits (impossible with limited budget)
  • Plurality across many small preferences beats concentrated plutocratic spending

QV vs. 1-Token-1-Vote

Property 1T1V (Standard DAO) Quadratic Voting
Whale dominance Complete (10M tokens = 10M votes) Reduced (10M tokens ≠ 3162² votes each)
Minority preference expression Near zero Enabled
Sybil resistance N/A (not identity-based) Requires verified identity
Implementation simplicity High Moderate
Real-world deployments Ubiquitous Limited; mostly experimental

Quadratic Funding (QF)

Vitalik Buterin extended QV into Quadratic Funding — a mechanism for allocating public goods funding:

Algorithm:

  1. Individuals donate any amount to projects they support
  2. A matching pool fund is distributed to projects proportional to the square of the sum of square roots of individual contributions

Example: Project A gets 100 donors giving $1 each vs. Project B gets 1 donor giving $100 each.

  • Project A: (√1 × 100)² = (10)² = $100 base + matching
  • Project B: (√100 × 1)² = (10)² = $100 base + matching

They receive equal matching despite equal total donations — because QF rewards breadth of support (many small donors) over depth (few large donors).

This implies: a grassroots project with 1000 backers at $1 each beats a corporate-sponsored project with 1 backer at $1000 in matching funds.


Gitcoin Grants — QF in Practice

Gitcoin is the largest real-world deployment of Quadratic Funding:

  • Runs “Grants Rounds” where anyone can submit a project (open source software, public goods, DeFi protocols)
  • Community donates any amount from any wallet
  • Matching pool (funded by Gitcoin, Optimism, Ethereum Foundation, sponsors) is distributed via QF algorithm
  • Over $50M allocated using QF mechanisms across multiple rounds

Results: Small open-source projects with large communities (but small average donations) consistently win significant matching funds that pure donation-size mechanisms would not favor.


Sybil Problem

QF/QV requires counting people, not dollars — which means it’s vulnerable to Sybil attacks: one person creates 1000 fake wallets and donates $0.01 each = massive QF matching power.

Solutions:

  • Gitcoin Passport: Aggregates identity “stamps” (Twitter, GitHub, ENS, Proof of Humanity) into a trust score; gates QF eligibility
  • World ID (Worldcoin): Biometric proof-of-personhood; one person = one verified World ID
  • MACI (Minimum Anti-Collusion Infrastructure): ZK-proof based voting system that makes bribery/collusion provably impossible

Deployments in DAO Governance

Optimism Collective:

  • Retroactive Public Goods Funding (RPGF) uses a combination of token holder voting and citizen house mechanisms inspired by QV principles
  • The “Citizens House” is specifically designed to incorporate non-token-weighted voice

Gitcoin DAO:

  • Uses both QF for grants allocation and quadratic voting experiments for governance decisions

RadicalxChange Foundation:

  • Organization founded by Glen Weyl; runs QV experiments in academic and civic contexts

Social Media Sentiment

Quadratic voting and QF are discussed in academic and governance-focused CT circles and Ethereum governance forums. Gitcoin Grants rounds using QF generate engagement among Ethereum public goods advocates. Mainstream CT is largely unaware of QV mechanics; sybil vulnerability is the main counterargument raised by skeptics.


Last updated: 2026-04

Related Terms


Sources

Weyl, E. G. (2017). Quadratic Voting as Efficient Corporate Governance. University of Chicago Law Review.

Buterin, V., Hitzig, Z., & Weyl, E. G. (2019). A Flexible Design for Funding Public Goods. Management Science.

Posner, E. A., & Weyl, E. G. (2018). Radical Markets: Uprooting Capitalism and Democracy for a Just Society. Princeton University Press.

Laslier, J. F., et al. (2019). Are Quadratic Voting and Prediction Markets Compatible? arXiv.

Gitcoin Holdings. (2023). Gitcoin Grants: Impact Report and QF Allocation Analysis. Gitcoin Blog.