Onchain Atlas

Quadratic Voting

A voting system where casting extra votes on the same option costs progressively more, so strong preferences are heard without letting whales dominate every decision.

Also called: QV · quadratic funding voting · cost-squared voting

What it is

Quadratic voting lets participants express not just which option they prefer, but how strongly, while making it mathematically expensive to dominate a single decision. Each additional vote on the same choice costs the square of the number of votes cast — so 1 vote costs 1 "credit," 2 votes cost 4 credits, 3 votes cost 9 credits, and so on — spent from a fixed budget of voting credits each participant is given.

How it works

  1. Every participant is allocated a fixed budget of voting credits (or tokens) for a given decision or funding round.
  2. For each option or proposal, a participant chooses how many votes to allocate, and the credits spent equal the number of votes squared (n votes costs n² credits).
  3. This pricing curve means casting a single extra vote on an option you already voted for gets steadily more expensive, discouraging piling all your budget onto one choice.
  4. Participants instead tend to spread credits across several proposals they care about, or concentrate heavily only on the few they feel strongest about, accepting the quadratic cost.
  5. Votes across all participants are tallied per option (summing raw vote counts, not credits spent), and the highest-tallied options win or receive proportional funding.
  6. In quadratic funding variants (grant matching), the mechanism instead uses the sum-of-square-roots-then-squared formula across many small contributors to compute a matching pool allocation, rewarding proposals with broad small-donor support over those with a single large donor.
  7. Sybil resistance (proving each participant is a unique, un-duplicated identity) is a prerequisite, since splitting one identity into many resets everyone's cheap first vote.

Why designers use it

  • Lets intensity of preference matter, unlike one-person-one-vote which can't distinguish "slightly prefer" from "desperately need."
  • Blunts whale dominance relative to simple token-weighted voting, since buying overwhelming influence over one decision costs quadratically more, not linearly more.
  • In grant funding, rewards proposals with genuine broad community support over ones bankrolled by a single wealthy backer.
  • Produces more efficient aggregate outcomes in public-goods-style decisions where preference intensity carries real information.

Failure modes

  • Sybil attacks are the central threat: without robust unique-identity verification, one actor splitting into many wallets gets many "cheap" first votes instead of paying the quadratic cost, and the whole mechanism's guarantee collapses.
  • Collusion rings: coordinated groups can pool resources and split votes across many colluding identities to simulate broad organic support in quadratic funding rounds.
  • Identity verification is hard and often invasive (KYC, biometrics, social graphs), trading a plutocracy problem for a privacy or gatekeeping problem.
  • Voter confusion: the quadratic cost curve is unintuitive to most participants, leading to suboptimal or accidental vote allocation compared to simpler mechanisms.
  • Gameable in small populations: with few participants, a single sophisticated voter who understands the math can still exert outsized influence over naive voters who don't budget their credits well.

What to check before using it

  • What sybil resistance mechanism is actually in place (proof-of-personhood, social attestation, stake-based identity), and how well does it hold up against a motivated attacker?
  • Is the credit budget and cost curve clearly explained to participants so votes reflect genuine preference rather than confusion?
  • For funding rounds, is there collusion detection or anti-fraud tooling to catch coordinated small-donor rings gaming the matching formula?
  • Is the population large and diverse enough for the statistical benefits of quadratic aggregation to actually hold, or is it a small enough group that gaming dominates?
  • What's the fallback if identity verification fails or excludes legitimate participants (accessibility, false negatives)?

Experiments that used it · 2

Shown oldest first, so you can watch the design evolve.

Colorado Quadratic Voting
The Colorado House Democratic caucus used quadratic voting from 2019–2023 to prioritize budget bills — the first use of QV inside a US legislature — before the anonymous-ballot format was discontinued in 2024 over conflict with open-meetings transparency requirements.
2019 partial success
Optimism Retro Funding
Optimism's retroactive public goods funding program that pays contributors in OP tokens for impact already delivered, as judged by a rotating body of 'badgeholder' voters.
2022 partial success