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

TL;DR

This paper proves that no permissionless blockchain voting rule based solely on wallet balance can prevent Sybil attacks, showing that even dampening mechanisms like quadratic voting are vulnerable to large-scale manipulation.

Contribution

The authors formally demonstrate the impossibility of anti-plutocratic governance rules in permissionless blockchains and quantify the vulnerability of common voting schemes through real-world DAO analysis.

Findings

Sybil attacks can amplify voting power by over 4,000 times under quadratic voting.

Real DAO proposal data shows attack costs are much lower than the value at stake.

Concave voting rules still allow linear growth in voting power through splitting strategies.

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-($\beta = 0.25$) 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.