Quadratic Voting

The core mathematical principle where the cost of casting n votes for a single option is n² voice credits. This creates a diminishing marginal utility for concentrated voting power.

• Example: 1 vote costs 1 credit, 2 votes cost 4 credits, 3 votes cost 9 credits.
• This structure makes it exponentially expensive for a single participant to dominate an outcome, forcing strategic allocation of a limited budget.

Each participant receives an equal, fixed budget of voice credits to spend across all proposals or candidates. This establishes a foundation of one-person-one-vote equality in budget, not in vote distribution.

• The budget constraint forces voters to make trade-offs, signaling which issues they care about most.
• It prevents Sybil attacks by capping influence per wallet or identity, as creating multiple identities does not increase the total budget.

QV allows voters to signal the strength of their preferences, not just binary approval/disapproval. A voter who feels strongly about a proposal can spend a large portion of their budget on it, but at a steep quadratic cost.

• This generates more nuanced data than simple majority voting, revealing collective welfare and the intensity of minority opinions.
• It helps surface proposals with broad, mild support versus those with narrow, passionate support.

The quadratic cost function is a mathematical defense against plurality tyranny and whale dominance.

• It is economically irrational for a wealthy or highly motivated actor to buy enough votes to swing an outcome, as the cost becomes prohibitive.
• This makes QV collusion-resistant; forming a cartel to concentrate votes on a single option is financially inefficient compared to distributing support.

A direct application of QV principles for public goods funding. In Quadratic Funding, the amount matched to a project is proportional to the square of the sum of the square roots of contributions.

• This algorithm optimally allocates a matching pool to projects based on the breadth of support (number of contributors) rather than the depth (total amount).
• A project with 100 contributors of $1 each receives far more in matching funds than a project with 1 contributor of $100, maximizing democratic utility.

Practical QV requires a Sybil-resistant identity system to prevent users from splitting their budget across multiple fake identities. Common solutions include:

• Proof of Personhood (e.g., BrightID, Worldcoin)
• Social graph analysis and trust networks
• Plurality of identity attestations Without this, the one-person-one-budget principle fails, and the system reverts to a quadratic cost plutocracy.

A core requirement for effective QV is Sybil resistance—preventing a single entity from creating many identities to game the system.

• Solutions: Projects use proof-of-personhood (e.g., BrightID), soulbound tokens, or reputation-based whitelists to ensure one-human-one-vote-power foundations.
• Consequence: Without robust Sybil resistance, QV can be manipulated, undermining its egalitarian goals.

QV is often contrasted with the dominant token-weighted voting model.

• Token-Weighted: Voting power is directly proportional to token holdings (1 token = 1 vote). This can lead to plutocracy.
• Quadratic Voting: Voting power increases with the square root of capital spent, diluting the influence of concentrated wealth. It measures intensity of preference, not just capital weight.

Unlike one-person-one-vote, QV allows participants to express the strength of their preferences by purchasing additional votes on an issue. The quadratic cost function (cost = votes²) makes buying many votes prohibitively expensive, forcing voters to allocate their budget across issues they care about most. This reveals not just binary preference but marginal value, leading to decisions that maximize aggregate welfare.

QV provides inherent resistance to both Sybil attacks (creating fake identities) and plutocracy (rule by the wealthy).

• Sybil Resistance: An attacker must square the cost for votes across each fake identity, making large-scale manipulation economically irrational.
• Plutocracy Resistance: While a wealthy entity can buy more votes, the quadratic cost ensures their influence grows linearly with spending, not exponentially. Doubling votes quadruples the cost, preventing outright purchase of outcomes.

A direct application in public goods funding, Quadratic Funding is a mechanism where the matching subsidy for a project is proportional to the square of the sum of the square roots of contributions. This optimally allocates a matching pool based on the number of unique contributors rather than the total amount, democratizing funding. It creates a matching curve that favors projects with broad, grassroots support over those backed by a few large whales.

By forcing voters to budget their voting credits, QV incentivizes compromise and reduces binary, winner-take-all outcomes. A voter with a strong preference on one issue must spend credits that could be used elsewhere, encouraging them to support moderate positions on other issues. This leads to more nuanced governance and can help surface Pareto-improving proposals that benefit a broad majority, rather than catering to intense minorities.

QV's advantages are grounded in economic theory. Under idealized conditions (cardinal utilities, perfect information), it is proven to maximize the sum of utilities of the participants, a concept known as optimal collective choice. It aligns individual incentives with group welfare, making it a strategy-proof mechanism in the sense that honest voting is the optimal strategy for most participants, reducing tactical manipulation.

The core principle of Quadratic Voting—that the cost of votes scales quadratically—is easily undermined if a single entity can create multiple identities (sybils). Without robust identity verification, an attacker can split their capital across many accounts to gain disproportionate influence at a linear cost. This necessitates sybil-resistance mechanisms like proof-of-personhood, social graph analysis, or bonded identities, which themselves add complexity and potential centralization vectors.

The financial cost of voting, even if quadratic, can create significant barriers to entry. This can lead to low voter turnout or skew governance toward wealthier participants, undermining the goal of capturing the "wisdom of the crowd." Furthermore, the cognitive load of calculating optimal quadratic vote allocations (vote budgeting) can deter casual participants. Projects often use subsidized voting credits instead of real tokens to mitigate this, but this decouples the vote from direct economic stake.

QV is theoretically resistant to simple vote buying, as the quadratic cost makes purchasing many votes for a single option prohibitively expensive. However, sophisticated collusion schemes can circumvent this. For example, participants can coordinate to reciprocally fund each other's votes on preferred outcomes or use bribery schemes that refund the quadratic cost to voters, effectively converting the system back to linear voting. Detecting and preventing such covert coordination is a significant practical challenge.

The user experience for Quadratic Voting is inherently more complex than simple yes/no voting. Interfaces must clearly communicate:

• The quadratic cost curve.
• How to allocate a budget of voting credits.
• The real-time impact of each additional vote. Poor UX can lead to voter error and frustration. Furthermore, tallying results and proving their correctness off-chain requires more computational work than a simple sum, adding overhead for result verification and dispute resolution.

A critical design decision is determining what token or credit is used to pay for votes. Using the native governance token aligns voting power with economic stake but exacerbates wealth concentration issues. Using a non-transferable voting credit (e.g., one per identity) promotes equality but severs the link to stakeholding. Using a separate fee token introduces exchange rate complexities. The choice fundamentally shapes the electorate and the system's resistance to manipulation.

Most real-world QV implementations, such as in Gitcoin Grants or some DAOs, are approximations of the ideal model. Common simplifications include:

• Using a finite budget of credits instead of a continuous quadratic payment.
• Applying the quadratic formula to the sum of votes per project, not per voter.
• Running votes over discrete rounds rather than continuously. These adaptations make the system more practical but can dilute the theoretical guarantees of preference revelation and efficiency.

The standard 'one-person, one-vote' system where each participant casts a single, undifferentiated vote for their preferred option. This is the baseline contrast to Quadratic Voting, as it fails to capture preference intensity and is susceptible to the tyranny of the majority. In blockchain governance, simple token-weighted voting (1 token = 1 vote) is a form of plurality voting that can lead to plutocratic outcomes.

A continuous decision-making system where voters stake tokens on proposals over time, with their voting power ('conviction') accumulating the longer their tokens remain committed. It is designed for funding public goods and ongoing governance, using time as a proxy for preference intensity. Unlike Quadratic Voting's snapshot-in-time budget, it allows for dynamic preference signaling and reduces the need for frequent proposal cycles.

• Key Feature: Voting power grows logarithmically with time staked.
• Use Case: Prominently used in the Commons Stack framework and Giveth.

The budget of influence allocated to each participant in a Quadratic Voting round. These are not directly equivalent to tokens or currency; they are a synthetic accounting unit used solely for voting. A participant might receive 99 voice credits to allocate across multiple proposals. The quadratic cost function applies to the use of these credits: spending n votes on one option costs n² credits.

The security property of a system that prevents a single entity from creating many fake identities (Sybils) to manipulate outcomes. Quadratic Voting's cost structure is vulnerable to Sybil attacks if identity is cheap to create, as an attacker could split their budget across many identities for linear influence. Effective QV implementations require a robust identity layer (like proof-of-personhood or social graph analysis) to issue voice credits per unique human.

An economic concept describing the challenge of accurately eliciting how much individuals truly value a good or outcome. Quadratic Voting is a mechanism design solution to this problem. By making the marginal cost of votes increase, it forces voters to strategically allocate their limited voice credits, theoretically revealing a more honest aggregate of the community's weighted preferences compared to simple voting.