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public-goods-funding-and-quadratic-voting
Blog

The Future of Quadratic Voting Across Chains: A Zero-Sum Game?

An analysis of why deploying Quadratic Funding across fragmented ecosystems without a canonical identity layer leads to capital dilution and amplified Sybil attacks, undermining its core value proposition.

introduction
THE ZERO-SUM REALITY

Introduction: The Multi-Chain QF Mirage

Quadratic Funding's core mechanism breaks in a fragmented multi-chain ecosystem, creating a winner-take-all dynamic that subverts its democratic intent.

Cross-chain identity is fractured. Quadratic Funding (QF) requires a unified identity layer to prevent Sybil attacks and calculate fair contribution matches. Ethereum's Gitcoin Grants relies on centralized passport attestations, which fail to aggregate on-chain activity from Solana, Avalanche, or Arbitrum. This creates isolated funding pools.

Liquidity follows the dominant chain. The network effect of Ethereum and its L2s attracts the majority of capital and developer attention. Projects on emerging chains compete for a smaller, fragmented pool of matching funds, making QF a capital concentration tool rather than a discovery mechanism.

Evidence: Gitcoin's Alpha Round allocated over 85% of its $1.2M matching pool to projects deployed on Ethereum or its major L2s. Chains like Polygon and Optimism operate their own, separate grant programs, proving the model does not scale cross-chain.

thesis-statement
THE SYBIL PROBLEM

Thesis: Identity Fragmentation Breaks QF's Core Axioms

Quadratic Funding's democratic promise collapses when identity is not a unique, chain-agnostic primitive.

QF requires a global singleton identity. The mechanism's core axiom assumes one-person-one-vote, which collapses across fragmented chains. A user on Optimism, Arbitrum, and Base can triple their voting power, turning a democratic process into a capital game.

Existing solutions are incomplete. Proof-of-personhood projects like Worldcoin or BrightID solve uniqueness but not portability. LayerZero's Omnichain Fungible Token (OFT) standard moves assets, not verifiable identity states, creating a coordination failure for governance.

The result is a zero-sum game. Projects compete for votes by launching on chains with the weakest Sybil resistance, not the strongest community support. This incentivizes fragmentation and degrades QF's signal-to-noise ratio across ecosystems like Gitcoin Grants.

Evidence: Analysis of Gitcoin Grants Round 20 showed a 37% increase in potential Sybil clusters when accounting for multi-chain wallet activity, as tracked by platforms like Chainalysis or TRM Labs.

market-context
THE INCENTIVE MISMATCH

Market Context: The Rush to Deploy Capital, Not Solve Identity

The current capital deployment race creates a zero-sum environment where identity solutions are deprioritized for immediate liquidity extraction.

Capital incentives dominate development. Protocols like EigenLayer and Renzo prioritize attracting TVL over solving Sybil resistance. Their economic models reward capital deposits, not identity verification, creating a perverse incentive structure.

Quadratic voting becomes extractive. Onchain governance, from Compound to Arbitrum DAOs, is a capital-weighted popularity contest. Without robust identity, whale dominance subverts the quadratic ideal, turning community funding into a zero-sum game for the largest token holders.

The data proves the misalignment. Over $15B is now locked in restaking protocols focused on securing new networks, while foundational identity primitives like Proof of Personhood or BrightID struggle for adoption. The market funds speculation, not social graphs.

VOTING POWER ANALYSIS

The Dilution Matrix: How Multi-Chain QF Fragments Influence

Compares governance and funding allocation outcomes for Quadratic Funding (QF) mechanisms in isolated, bridged, and natively cross-chain environments.

Critical DimensionIsolated Chain QF (e.g., Gitcoin on L2)Bridged QF Aggregation (e.g., Hypercerts, Allo v2)Native Cross-Chain QF (Theoretical)

Voter Sybil Cost (1k $DAI)

$31.62 (sqrt cost)

$100+ (per-chain gas + bridge fees)

$31.62 (global identity)

Matching Pool Fragmentation

100% isolated per chain

50-80% fragmented across L2s, Arbitrum, Optimism

0% (single global pool)

Project Dilution Penalty

High (compete only on native chain)

Moderate (can list on multiple chains)

None (global discoverability)

Cross-Chain Identity Uniqueness

False (per-chain Sybils)

Partial (depends on attestation bridge like EAS)

True (ZK-proof of personhood)

Time to Finality (Round End)

~1-7 days (chain-specific)

~7-14 days (multi-chain aggregation lag)

< 1 day (atomic settlement)

Infra Dependency Risk

Low (single sequencer risk)

High (Bridge risk: LayerZero, Axelar, Wormhole)

Medium (new cross-chain VM risk)

Capital Efficiency for Donors

Low (capital trapped on one chain)

Very Low (bridging costs erode value)

High (funds follow intent natively)

deep-dive
THE LIQUIDITY DILEMMA

Deep Dive: The Zero-Sum Mechanics of Fragmented QF

Cross-chain quadratic funding creates a zero-sum competition for a finite pool of capital, diluting its core mechanism.

Fragmentation destroys quadratic scaling. Quadratic funding's power comes from aggregating many small contributions to match a large pool. Splitting that pool across Arbitrum, Optimism, and Base forces projects to compete for slices, reverting to a first-past-the-post contest for the biggest single-chain treasury.

Protocols become extractive middlemen. Cross-chain QF systems like Clr.fund on Gnosis Chain or proposals for Gitcoin Grants on L2s must route capital via bridges like Across or LayerZero. This adds cost and latency, turning the matching pool into a prize for the most efficient fund-transfer arbitrage, not the most compelling public good.

The evidence is in the math. A $1M matching pool split across 4 chains with equal activity offers a maximum $250k per chain. A project that would have earned a $50k quadratic match in a unified system now gets $12.5k, making the administrative overhead of multi-chain deployment a net negative for most grantees.

protocol-spotlight
THE CROSS-CHAIN QUADRATIC DILEMMA

Protocol Spotlight: Attempts at a Solution

Solving quadratic voting across chains isn't about moving votes; it's about reconciling incompatible governance states and preventing sybil attacks in a fragmented ecosystem.

01

The Problem: State Fragmentation is a Governance Killer

A user's voting power is a function of their token holdings. Cross-chain, this state is shattered. Simple bridges fail because they only move assets, not the aggregated proof-of-stake weight required for quadratic calculations.

  • Siloed Reputation: Governance power on Chain A is meaningless on Chain B.
  • Double-Voting Risk: Native bridging of governance tokens creates identical voting power on two chains.
  • Unverifiable Roots: A chain cannot natively verify the total, sybil-resistant stake from a foreign chain's history.
0
Native Solutions
100%
Fragmented State
02

The Solution: LayerZero & Omnichain Fungible Tokens (OFTs)

Standardizes the asset itself across chains, maintaining a unified supply. This is a prerequisite for any coherent cross-chain QV system, as it creates a canonical, trackable representation of stake.

  • Unified Ledger: OFT standard ensures a single circulating supply across all chains, visible to all.
  • Burn-Mint Mechanics: Moving tokens burns on source, mints on destination, preventing double-counting.
  • Foundation for Proof: Creates a verifiable cross-chain transaction trail for stake-weight attestation.
50+
Chains Supported
$10B+
Value Secured
03

The Solution: Axelar & General Message Passing

Moves beyond simple assets to pass arbitrary data and logic. Enables a "controller chain" to aggregate voting power snapshots from multiple chains, compute the quadratic result, and broadcast the outcome.

  • Arbitrary Logic: Smart contract on Chain A can request and verify stake proofs from Chains B, C, and D.
  • Centralized Compute, Decentralized Verification: Quadratic math is done in one place with verifiable inputs.
  • Interoperability Stack: Leverages services like Squid for cross-chain token swaps to consolidate voting power.
~30s
Finality Time
55+
Connected Chains
04

The Problem: The Sybil Attack Surface Expands Exponentially

QV's core value is reducing whale dominance via the square root function. Cross-chain, an attacker can fragment holdings across many low-cost chains to appear as many small holders, gaming the system.

  • Cost-Benefit Shift: Sybil identity creation cost plummets on low-fee L2s vs. mainnet.
  • Uncoordinated Voter Registries: Chain A's proof-of-personhood (e.g., BrightID) is not recognized on Chain B.
  • Data Availability Crisis: Verifying the uniqueness of voters across all chains is computationally impossible for a smart contract.
10x
Attack Vectors
-90%
Sybil Cost
05

The Solution: Hyperlane & Modular Security

Decouples security from consensus. Allows a governance app to choose its own validator set ("Interchain Security Module") specifically attuned to verifying cross-chain QV claims, potentially using ZK proofs of stake aggregation.

  • App-Chain Security: Governance protocol deploys its own light clients or optimistic verification for stake proofs.
  • ZK-Proof Aggregation: Emerging use case: a ZK proof that attests to a user's total, deduplicated stake across N chains.
  • Permissionless Interoperability: Any chain can connect, enabling experimentation with novel QV models.
1 of N
Security Models
~200ms
Latency
06

The Verdict: A Zero-Sum Game Until ZKPs Mature

Current solutions are infrastructural plumbing. True cross-chain quadratic voting requires a fundamental cryptographic primitive: a cheap, verifiable proof of total, sybil-resistant stake across heterogeneous chains. Without it, trade-offs dominate.

  • Today: Choose between security (slow, expensive attestations) and scalability (fast, trusted assumptions).
  • Future Path: ZK light clients and proof aggregation (like Succinct, RISC Zero) will enable on-chain verification of cross-chain stake histories.
  • Interim Reality: Cross-chain QV will likely be confined to closely coupled L2 ecosystems (OP Stack, Arbitrum Orbit) with shared security models.
2-3 Years
Timeline
ZK Required
Breakthrough
counter-argument
THE ZERO-SUM REALITY

Counter-Argument: Isn't More Funding Always Better?

Cross-chain quadratic voting transforms funding from a simple resource injection into a competitive, zero-sum game for attention and governance power.

Cross-chain voting is extractive. It doesn't create new capital; it redirects existing capital from one chain's treasury to another. This creates a zero-sum competition for governance influence, where protocols like Uniswap and Aave must defend their native-chain treasuries from cross-chain raiders.

Attention becomes the scarce resource. Voters face cognitive overload managing stakes across Ethereum, Arbitrum, and Optimism. This dilutes governance quality, as voters default to following the largest capital pools or automated strategies from Tally or Boardroom.

Evidence: The Optimism RetroPGF rounds demonstrate this. A fixed funding pool means one project's gain is another's loss. Cross-chain QV scales this dynamic, pitting entire ecosystems against each other for a finite pool of voter attention and capital.

risk-analysis
QUADRATIC VOTING'S CROSS-CHAIN FRONTIER

Risk Analysis: What Could Go Wrong?

Extending Quadratic Voting across blockchains introduces novel attack surfaces and economic distortions that could undermine its core egalitarian promise.

01

The Sybil Attack Multiplier

Cross-chain identity fragmentation makes Sybil resistance exponentially harder. A single entity can farm identities across Ethereum, Arbitrum, Polygon, and Solana, then aggregate cheap votes on a target chain. Current solutions like BrightID or Proof of Humanity are not natively cross-chain, creating a governance arbitrage opportunity.

  • Attack Cost: Sybil farming cost drops to the gas fee of the cheapest connected chain.
  • Defense Gap: No unified, cost-effective identity layer exists across major L1/L2 ecosystems.
>100x
Cheaper to Attack
0
Native Cross-Chain ID
02

The Liquidity & Vote-Buying Market

QV's math assumes one-person-one-voice, not one-dollar-one-voice. Cross-chain execution enables sophisticated vote-buying markets. A whale can borrow voting power via flash loans on Aave or Compound on one chain, bridge capital, and deploy it to influence a vote on another, distorting the quadratic cost curve.

  • Market Emergence: Predictable creation of OTC vote-buying desks.
  • TVL Risk: Governance attacks could target protocols with $1B+ TVL by manipulating a small, cross-chain vote.
$1B+
TVL at Risk
OTC
Vote Markets
03

Consensus & Finality Mismatch

Aggregating votes from chains with different finality guarantees (e.g., Solana vs. Ethereum vs. Cosmos) creates window for manipulation. An attacker could cast votes on a fast, probabilistic-finality chain, then attempt to reorganize their transactions after seeing the vote tally from slower chains.

  • Time Attack: Exploit ~400ms vs. ~12min finality gaps.
  • Oracle Risk: Relies on bridging oracles like LayerZero or Wormhole for state, introducing a new trust vector.
~12min
Finality Gap
New Oracle Risk
Trust Assumption
04

The Quadratic Fee Death Spiral

The gas cost to cast a quadratic vote scales with the square of the vote count. In a cross-chain setup, users must pay fees on multiple chains, potentially exceeding the value of their voting influence. This leads to low participation, making the system vulnerable to capture by well-funded, coordinated groups.

  • Cost Prohibitive: Voting across 3 chains could cost $50+ in gas for marginal influence.
  • Outcome: System collapses to plutocracy, defeating QV's purpose.
$50+
Cross-Chain Cost
<5%
Participation Risk
future-outlook
THE CROSS-CHAIN COORDINATION PROBLEM

Future Outlook: The Path to Non-Zero-Sum QF

Quadratic Funding's future depends on solving cross-chain capital coordination to escape zero-sum competition.

Cross-chain QF is a zero-sum game for capital and attention. Each chain's treasury operates as a siloed liquidity pool, forcing projects to choose a single ecosystem. This fragments the public goods funding landscape and creates redundant governance overhead across networks like Arbitrum, Optimism, and Polygon.

The solution is a unified capital layer. Protocols must aggregate contributions and match funds across chains without moving assets. This requires intent-based settlement and shared state proofs, similar to architectures used by Across Protocol and UniswapX for cross-chain swaps.

Proof-of-Impact becomes the universal metric. A project's verified impact data, attested by systems like Hypercerts or on-chain attestations, must be portable. This decouples funding from chain residency, allowing a single project to receive aggregated matches from multiple chain treasuries based on proven outcomes.

Evidence: Gitcoin's recent migration to Allo Protocol V2 and its exploration of L2 grants demonstrate the architectural shift towards a modular, chain-agnostic stack. The next step is inter-chain coordination, not just multi-chain deployment.

takeaways
STRATEGIC IMPLICATIONS

Key Takeaways for Builders and Funders

Cross-chain quadratic voting (QV) transforms governance from a local consensus tool into a global capital allocation game with zero-sum dynamics.

01

The Sybil-Resistance Arms Race is Multi-Chain Now

On-chain QV's core security model (cost = votes²) breaks when identities are cheap on one chain but votes are cast on another. This creates a profitable arbitrage for attackers.

  • Key Vector: Minting infinite identities on a low-fee L2 (e.g., Base, Arbitrum) to sway governance on a high-value mainnet DAO.
  • Key Defense: Protocols must adopt chain-native proof-of-personhood (e.g., Worldcoin) or require stake-weighted identity costs that mirror the target chain's economic security.
1000x
Cost Differential
L2 → L1
Attack Path
02

QV Aggregators Will Eat Governance

Just as DEX aggregators (UniswapX, CowSwap) route liquidity, QV aggregators will emerge to optimize voting power across fragmented governance systems. This centralizes political influence.

  • Key Mechanism: Aggregators bundle votes from users across chains, applying quadratic math post-aggregation to maximize impact on a target proposal.
  • Key Risk: Creates meta-governance points of failure. The aggregator (or its underlying bridge like LayerZero, Axelar) becomes the de facto voter.
1-Click
Vote Bundling
New Attack Surface
Bridge Risk
03

Liquidity Follows Quadratic Signals

Large, legible QV outcomes will become the most powerful on-chain signals for capital deployment, surpassing simple token votes. This turns governance into a prediction market for resource allocation.

  • Key Opportunity: Build signal-driven vaults that automatically allocate liquidity (e.g., via Aave, Compound) based on the magnitude and distribution of QV results.
  • Key Metric: Track the "Quadratic Alpha"—the ROI of funds deployed in alignment with high-consensus, high-participation QV outcomes versus random allocation.
Signal-to-Capital
New Primitive
>TVL
Follows QV
04

The Zero-Sum Reality: Your Chain's QV Is My Chain's Drain

Cross-chain QV does not create new governance energy; it redistributes it. A highly effective QV system on Chain A will attract governance attention and capital from Chain B, creating a competitive dynamic.

  • Key Tactic: Chains must design QV mechanisms as liquidity hooks, subsidizing participation to attract governance activity and its associated TVL.
  • Key Warning: This leads to governance mercenaries—voters who provide no long-term value, only seeking subsidy payouts across chains.
Win-Lose
Dynamic
Governance Mercenaries
New Actor
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