Paper 2025/803

Universally Composable On-Chain Quadratic Voting for Liquid Democracy

Abstract

Decentralized governance plays a critical role in blockchain communities, allowing stakeholders to shape the evolution of platforms such as Cardano, Gitcoin, Aragon, and MakerDAO through distributed voting on proposed projects in order to support the most beneficial of them. In this context, numerous voting protocols for decentralized decision-making have been developed, enabling secure and verifiable voting on individual projects (proposals). However, these protocols are not designed to support more advanced models such as quadratic voting (QV), where the voting power, defined as the square root of a voter’s stake, must be distributed among the selected by voter projects. Simply executing multiple instances of a single-choice voting scheme in parallel is insufficient, as it can not enforce correct voting power splitting. To address this, we propose an efficient blockchain-based voting protocol that supports liquid democracy under the QV model, while ensuring voter privacy, fairness and verifiability of the voting results. In our scheme, voters can delegate their votes to trusted representatives (delegates), while having the ability to distribute their voting power across selected projects. We model our protocol in the Universal Composability framework and formally prove its UC-security under the Decisional Diffie–Hellman (DDH) assumption. To evaluate the performance of our protocol, we developed a prototype implementation and conducted performance testing. The results show that the size and processing time of a delegate’s ballot scale linearly with the number of projects, while a voter’s ballot scales linearly with both the number of projects and the number of available delegation options. In a representative setting with 64 voters, 128 delegates and 128 projects, the overall traffic amounts to approximately 2.7 MB per voted project, confirming the practicality of our protocol for modern blockchain-based governance systems.