An Empirical Evaluation of Quadratic Voting Counterfactuals in Token-weighted Governance: A Case Study of the Arbitrum DAO

Most decentralized autonomous organizations (DAOs) use a 1-Token-1-Vote rule, allowing capital ownership to translate directly into governance power. This paper evaluates how a Quadratic Voting (QV)-inspired square-root reweighting counterfactual would affect voting outcomes in the Arbitrum DAO. For this, a time-paginated pipeline was developed to retrieve approximately 850,000 off-chain Snapshot vote records across fifteen of the DAO's highest-turnout proposals where each participating wallet's token-weighted voting power was replaced with its square root, and the proposal outcomes were recalculated. The results reveal extreme concentration of voting power, with a mean Gini coefficient of approximately 0.9950 among active participating wallets.

In some proposals, the ten largest participating wallets or delegates collectively controlled as much as 86.87% of the total voting weight. Consequently, square-root reweighting changed the winning outcome in four of the fifteen proposals (26.7% of this purposively-selected, high-turnout sample), demonstrating that these outcomes were sensitive to the distribution of voting power across wallets. Its effect on victory margins was heterogeneous: margins widened in six proposals and narrowed in nine, with changes ranging from a 55.90-percentage-point expansion to a 37.76-percentage-point contraction.

Notably, all four outcome reversals involved funding, grants, security expenditure, coalition financing, or related resource-allocation decisions. These findings suggest that square-root reweighting can alter both the magnitude and direction of token-weighted governance outcomes by reducing the relative influence of highly concentrated token holdings.