Title: Enhancing Decentralization in Blockchain Decision-Making Through Quadratic Voting and Its Generalization Show Chinese title

Title: 通过二次投票及其推广在区块链决策中增强去中心化

Abstract: This study explores the application of Quadratic Voting (QV) and its generalization to improve decentralization and effectiveness in blockchain governance systems. The conducted research identified three main types of quadratic (square root) voting. Two of them pertain to voting with a split stake, and one involves voting without splitting. In split stakes, Type 1 QV applies the square root to the total stake before distributing it among preferences, while Type 2 QV distributes the stake first and then applies the square root. In unsplit stakes (Type 3 QV), the square root of the total stake is allocated entirely to each preference. The presented formal proofs confirm that Types 2 and 3 QV, along with generalized models, enhance decentralization as measured by the Gini and Nakamoto coefficients. A pivotal discovery is the existence of a threshold stakeholder whose relative voting ratio increases under QV compared to linear voting, while smaller stakeholders also gain influence. The generalized QV model allows flexible adjustment of this threshold, enabling tailored decentralization levels. Maintaining fairness, QV ensures that stakeholders with higher stakes retain a proportionally greater voting ratio while redistributing influence to prevent excessive concentration. It is shown that to preserve fairness and robustness, QV must be implemented alongside privacy-preserving cryptographic voting protocols, as voters casting their ballots last could otherwise manipulate outcomes. The generalized QV model, proposed in this paper, enables algorithmic parametrization to achieve desired levels of decentralization for specific use cases. This flexibility makes it applicable across diverse domains, including user interaction with cryptocurrency platforms, facilitating community events and educational initiatives, and supporting charitable activities through decentralized decision-making. Show Chinese abstract

Abstract: 这项研究探讨了二次投票（QV）及其推广在区块链治理系统中提高去中心化和效率的应用。 进行的研究确定了三种主要类型的二次（平方根）投票。 其中两种涉及分拆权益的投票，一种涉及不分拆的投票。 在分拆权益中，类型1的QV在将权益分配到各个偏好之前对总权益取平方根，而类型2的QV则先分配权益，然后再取平方根。 在不分拆权益（类型3 QV）中，总权益的平方根被完全分配给每个偏好。 所提出的正式证明确认，类型2和3的QV以及推广模型，通过吉尼系数和中本系数衡量的去中心化程度有所提高。 一个关键发现是存在一个门槛权益持有人，其相对投票比例在QV下相比线性投票有所增加，同时较小的权益持有人也获得了影响力。 推广的QV模型允许灵活调整这一门槛，从而实现针对特定用例的定制化去中心化水平。 保持公平性，QV确保权益较高的利益相关者保留成比例更大的投票比例，同时重新分配影响力以防止过度集中。 研究表明，为了保持公平性和鲁棒性，QV必须与保护隐私的密码投票协议一起实施，否则最后投票的选民可能会操纵结果。 本文提出的推广QV模型允许算法参数化，以实现特定用例所需的去中心化水平。 这种灵活性使其适用于各种领域，包括用户与加密货币平台的互动，促进社区活动和教育倡议，以及通过去中心化决策支持慈善活动。