In traditional, one-vote-per-person voting systems, privacy equates with ballot secrecy: voting tallies are published, but individual voters' choices are concealed. Voting systems that weight votes in proportion to token holdings, though, are now prevalent in cryptocurrency and web3 systems. We show that these weighted-voting systems overturn existing notions of voter privacy. Our experiments demonstrate that even with secret ballots, publishing raw tallies often reveals voters' choices. Weighted voting thus requires a new framework for privacy. We introduce a notion called B-privacy whose basis is bribery, a key problem in voting systems today. B-privacy captures the economic cost to an adversary of bribing voters based on revealed voting tallies. We propose a mechanism to boost B-privacy by noising voting tallies. We prove bounds on its tradeoff between B-privacy and transparency, meaning reported-tally accuracy. Analyzing 3,582 proposals across 30 Decentralized Autonomous Organizations (DAOs), we find that the prevalence of large voters ("whales") limits the effectiveness of any B-Privacy-enhancing technique. However, our mechanism proves to be effective in cases without extreme voting weight concentration: among proposals requiring coalitions of $\geq5$ voters to flip outcomes, our mechanism raises B-privacy by a geometric mean factor of $4.1\times$. Our work offers the first principled guidance on transparency-privacy tradeoffs in weighted-voting systems, complementing existing approaches that focus on ballot secrecy and revealing fundamental constraints that voting weight concentration imposes on privacy mechanisms.

翻译：在传统的一人一票投票系统中，隐私等同于选票保密性：投票统计结果被公开，但个体选民的选择被隐藏。然而，在加密货币和Web3系统中，按代币持有量比例加权的投票系统现已普遍存在。我们证明，这些加权投票系统颠覆了现有的选民隐私概念。我们的实验表明，即使采用无记名投票，公布原始统计结果也常常会泄露选民的选择。因此，加权投票需要一种新的隐私框架。我们引入了一种称为B-隐私的概念，其基础是贿赂——当今投票系统中的关键问题。B-隐私捕捉了对手基于公开的投票统计结果贿赂选民所需的经济成本。我们提出了一种通过为投票统计添加噪声来增强B-隐私的机制。我们证明了该机制在B-隐私与透明度（即报告统计结果的准确性）之间权衡的理论界限。通过对30个去中心化自治组织（DAO）的3,582项提案进行分析，我们发现大型选民（"巨鲸"）的普遍存在限制了任何B-隐私增强技术的有效性。然而，我们的机制在投票权重未极端集中的情况下被证明是有效的：在需要≥5名选民组成联盟才能改变结果的提案中，我们的机制将B-隐私提高了4.1倍的几何平均因子。我们的工作首次为加权投票系统中的透明度-隐私权衡提供了原则性指导，补充了现有专注于选票保密性的方法，并揭示了投票权重集中对隐私机制施加的根本性约束。