Swimming with Whales: Analysis of Power Imbalances in Stake-Weighted Governance

TL;DR

This paper analyzes power imbalances in stake-weighted governance systems like Proof-of-Stake blockchains, using the Penrose-Banzhaf index, combining theoretical insights with empirical data from real-world on-chain governance.

Contribution

It provides analytical bounds on power-stake alignment and empirical analysis of power imbalances in a real blockchain governance system.

Findings

Perfect power-stake alignment is generally unattainable but can be approximated under certain conditions.

Empirical data from Project Catalyst reveals significant power imbalances in stake-weighted governance.

The Penrose-Banzhaf index effectively quantifies power disparities among stakeholders.

Abstract

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.