Square root voting, usually called quadratic voting, charges a voter the square of the influence they buy. One vote costs one credit, two votes cost four, three cost nine. The intent is to let someone who cares intensely about one question spend heavily there and pay for it everywhere else, rather than counting every voter the same on everything. It only behaves that way if each account is a distinct person.
The quadratic cost is charged per identity. Split one budget across ten accounts and the same total influence costs a tenth as much, which collapses the mechanism back into ordinary vote buying. Identity is not a deployment detail here. It is the mechanism.
The pricing rule, and what was actually proved
Lalley and Weyl set out the formal version in a Becker Friedman Institute working paper dated December 2015. Individuals buy votes in favor of their preferred alternative from a clearing house, paying the square of the number of votes purchased, and the sum of all votes purchased decides the outcome.1 Eric Posner's own summary adds the redistribution step: the money paid in is returned to voters on a per capita basis.2
The result they prove is narrower than the way it usually gets quoted. In an independent private-values environment, for any value distribution, all symmetric Bayes-Nash equilibria of quadratic voting converge toward efficiency in large populations, with waste decaying generically as one over N.1 That is an asymptotic statement under stated assumptions about how values are drawn. It is not a guarantee about any particular vote, and the paper itself carries Weyl's disclosure that he co-founded a company commercializing the mechanism.1 Both facts belong in the room when someone pitches it.
Voice credits, as it is actually run
Deployments phrase it as a budget rather than a purchase. Participants receive an allowance of voice credits and allocate them across the questions on a ballot, and the credits convert to counted votes by their square root: one credit is one vote, four credits are two votes, nine credits are three.3 Same curve, friendlier framing, and no money changes hands.
RadicalxChange's own reference page lists its case studies, among them the Colorado State Legislature and executive branch, the Nashville Metro Council and a New York City district.3 Look at what those have in common before you look at the results. Each is a closed roll of known people whose identities were established before anyone voted.
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The arithmetic that makes identity load-bearing
Work the cost through. Under a quadratic rule, casting v votes from one account costs v squared. Split those same v votes evenly across k accounts and each account pays v over k, squared, so the total across all of them is v squared divided by k. Ten accounts, one tenth the cost. A hundred accounts, one hundredth.
The penalty is assessed per account, not per person, so anyone who can create accounts cheaply converts a self-limiting cost curve into something close to linear. On a permissionless chain, accounts cost gas. That is the reason quadratic mechanisms in the wild are always paired with a personhood layer, and the reason a token-weighted DAO that adds a square root to its vote tally without adding identity has not made itself fairer. It has offered a volume discount to whoever splits first.
What this means for a token design
If you want quadratic voting, you are committing to run an identity system, and that system becomes the thing worth attacking. Whoever issues or scores personhood credentials holds the real power in the design, which is a centralization risk you have moved rather than removed, plus a privacy surface you now have to defend. Budget for it as a standing operation, not as a launch task.
Two boundaries worth naming. Quadratic voting prices votes for an individual spending from a budget. Quadratic funding is a different mechanism that computes matching funds across many contributors, and the two get conflated constantly; the sibling entry covers it. And on the business question underneath all of this, a fairer aggregation rule does not create demand for a token. It changes who decides. If holders are not voting today because the decisions do not affect their economics, changing the cost curve will not bring them back.
Common questions
What is quadratic voting in simple terms?
A voting rule where extra influence gets steadily more expensive. Each voter holds a budget of credits, and buying n votes on a question costs n squared credits, so votes cast equal the square root of credits spent.3 One credit buys one vote, nine buy three. The result is that a voter can express how strongly they feel about one issue, but only by giving up influence on the others.
Why does quadratic voting need identity verification?
Because the quadratic cost is charged per account. One actor splitting the same total votes across ten accounts pays a tenth of what a single account would pay, which turns the self-limiting cost curve into an almost linear one and returns the system to plain vote buying. On a permissionless chain, creating accounts costs almost nothing, so a personhood or sybil-resistance layer is a precondition rather than a hardening step.
Has quadratic voting been used in a real election?
It has been used for prioritization rather than binding public elections. RadicalxChange's reference page lists case studies including the Colorado State Legislature and executive branch, the Nashville Metro Council and a New York City district.3 Each of those runs on a closed roll of identified participants, which is the condition the mechanism depends on. We found no documented deployment on an open, permissionless identity set.
See Tokenomics Design for how this applies in practice.
Sources
- Quadratic Voting (Working Paper No. 2016-13)
Steven P. Lalley and E. Glen Weyl, Becker Friedman Institute, University of Chicago, 2015
Dated December 2015. Source for the payment rule, and for the proved result that symmetric Bayes-Nash equilibria converge toward efficiency in large populations with waste decaying generically as one over N. Weyl's disclosure of a commercial interest appears in the paper's first footnote. - Quadratic Voting
Eric Posner, 2015
Read 3 August 2026. Co-author's own restatement, including the detail that payments are returned to voters on a per capita basis. - Quadratic Voting (wiki entry)
RadicalxChange Foundation, 2026
Read 3 August 2026. Source for the voice credits framing and the square root conversion, and for the listed case studies: Colorado State Legislature and executive branch, Nashville Metro Council, NYC District 9 and the Colorado Climate Assemblies.
Last reviewed 2026-08
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