Voting methods weighted by stakes are the fundamental governance paradigm in Proof-of-Stake (PoS) blockchains. Such a paradigm is known to be prone to power distortions: a few users possessing large stakes may completely control decision making, even without owning the totality of the stakes. We study this phenomenon through the lens of computational social choice, focusing on the extent of power imbalances in stake-weighted voting when power is quantified using the Penrose-Banzhaf power index. Our work presents both analytical and empirical contributions. Analytically, we demonstrate that while a perfect alignment between power and relative stake ownership is generally unattainable, it can be approximated in expectation under specific conditions. Empirically, using data from a real-world on-chain governance system (Project Catalyst), we provide a more fine-grained understanding of the power imbalances that are likely to occur in current stake-weighted governance systems.

翻译：以权益加权的投票方式是权益证明（PoS）区块链的基本治理范式。已知此类范式易产生权力扭曲：少数持有大量权益的用户可能完全控制决策过程，即便其并未掌握全部权益。我们通过计算社会选择的视角研究该现象，重点关注当使用彭罗斯-班扎夫权力指数量化权力时，权益加权投票中权力失衡的程度。本研究兼具分析性与实证性贡献。在分析层面，我们证明虽然权力与相对权益持有量之间的完美对齐通常无法实现，但在特定条件下可在期望意义上近似达成。在实证层面，我们利用实际链上治理系统（Project Catalyst）的数据，对当前权益加权治理系统中可能出现的权力失衡提供了更精细化的理解。