Citation

Bennett, A., Vander Vos, P., Le, D. V., Belenkiy, M. “Concave is the New Linear: The Impossibility of Anti-Plutocratic DAO Governance.” arXiv:2605.18990v1 [cs.GT] (18 May 2026). Circle Research.

Core Result

No voting rule that derives power solely from wallet balance can be anti-plutocratic on a permissionless blockchain. Using a costed model of on-chain voting (per-wallet splitting + voting costs, fixed setup costs, minimum-balance requirements), they prove: whenever a wallet of any size yields nonzero voting power, a Sybil attacker who splits tokens across many wallets achieves total voting power that grows at least linearly in holdings. For concave rules actually proposed to dampen whales (positive, increasing, finite — e.g. Quadratic Voting), the optimal Sybil strategy yields power asymptotically linear in holdings, regardless of the cost scheme.

Why Concave Voting Fails

  • QV (power = √tokens) assumes one stable identity per voter; permissionless chains can’t bind wallets to identity, so the single-identity assumption breaks.
  • A Sybil attacker splits holdings into many wallets, each accruing the concave (cheap-per-token) low end of the curve, recovering ~linear aggregate power — defeating the anti-plutocratic intent. Anti-Sybil patches (minimum balances, higher voting/wallet-generation costs) don’t change the asymptotics.

Empirical Findings

  • Replayed the 10 most recent finalized proposals of 5 major DAOs (ENS, Compound, Uniswap, Arbitrum, ZKsync) under linear, quadratic, logarithmic, and power(α=0.25) voting.
  • Sybil amplification factors: 1,172×–4,039× under QV; >229,000× under steeper power rules.
  • Uniswap: a Sybil-optimal attacker captures a $300M vote for ~$75K in token + gas costs; a single-wallet attacker with the same budget gets only ~1/259 of the power needed to win.
  • Frames token-control attacks against the Feichtinger et al. SoK taxonomy (28 real-world attacks; bribing / token-control / HCI / code vulnerability), citing Tornado Cash DAO (2023) and Indexed Finance.

Connection to Wiki

See Also