Concave is the New Linear: The Impossibility of Anti-Plutocratic DAO Governance

2026-05-18

AI Summary

This study addresses a critical vulnerability in token-based voting mechanisms prevalent in DAO governance: despite proposals like quadratic voting designed to mitigate plutocratic control, such schemes remain susceptible to Sybil attacks on permissionless blockchains. The paper formally proves, for the first time, that any voting rule relying solely on wallet balances—defined by a regular, increasing, and bounded concave function—cannot resist Sybil manipulation, as effective voting power ultimately scales linearly with token holdings. By constructing an on-chain voting cost model incorporating splitting costs, setup overhead, and minimum balance constraints, and combining game-theoretic analysis with empirical backtesting on proposal data from five major Ethereum-based DAOs (including ENS and Compound), the authors demonstrate that quadratic voting exhibits Sybil amplification factors ranging from 1,172 to 4,039, and steeper power-law rules can exceed 229,000—rendering attack costs substantially lower than governance gains.

Abstract

Decentralized Autonomous Organizations (DAOs) run protocol governance by letting token holders vote on proposals. The dominant rule, voting power proportional to wallet balance, concentrates control among a small number of large holders, fueling the token-control governance attacks that have already compromised real protocols. To counter this concentration, the community has turned to anti-plutocratic voting mechanisms such as Quadratic Voting (QV), which assign sublinear voting power per token with the goal of dampening the influence of large holders. We prove that no voting rule that derives power solely from wallet balance can succeed on a permissionless blockchain. Through a costed model of on-chain voting that captures realistic blockchain frictions -- including per-wallet splitting and voting costs, fixed setup costs, and minimum-balance requirements -- we show that 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 their token holdings. For concave rules actually proposed to dampen governance power -- those that are positive, increasing, and finite -- we show that the optimal strategy yields power that is asymptotically linear in token holdings, regardless of the cost scheme. Instantiating the model on real DAOs reveals attack costs orders of magnitude below the value at stake. Replaying the ten most recent finalized proposals of five major DAOs (ENS, Compound, Uniswap, Arbitrum, and ZKsync) under linear, quadratic, logarithmic, and power-($β= 0.25$) voting, we measure Sybil amplification factors between $1,172\times$ and $4,039\times$ under Quadratic Voting, and exceeding $229,000\times$ under steeper power rules.

Problem

• DAO governance
• plutocracy
• Sybil attack
• voting mechanisms
• blockchain

Innovation

• Sybil attack
• anti-plutocratic governance
• concave voting rules
• DAO governance
• on-chain voting model