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How Does Stake Distribution Influence Consensus? Analyzing Blockchain Decentralization

Shashank Motepalli, Hans-Arno Jacobsen

TL;DR

The paper tackles the problem of insufficient decentralization in PoS/DPoS blockchains due to weight concentration among validators. It formalizes decentralization metrics for weighted consensus, conducts an empirical study of ten permissionless blockchains, and introduces the Square Root Stake Weight (SRSW) mechanism to rebalance staking influence without adding new tokens. The results show substantial improvements in decentralization: the Gini index improves by $37.16\%$ on average, while Nakamoto coefficients for liveness and safety rise by $101.04\%$ and $80.09\%$, respectively. This data-driven approach advances fairer stake distribution, enhances resilience against censorship, and reduces MEV risks, offering a practical path toward stronger decentralization in blockchain consensus.

Abstract

In the PoS blockchain landscape, the challenge of achieving full decentralization is often hindered by a disproportionate concentration of staked tokens among a few validators. This study analyses this challenge by first formalizing decentralization metrics for weighted consensus mechanisms. An empirical analysis across ten permissionless blockchains uncovers significant weight concentration among validators, underscoring the need for an equitable approach. To counter this, we introduce the Square Root Stake Weight (SRSW) model, which effectively recalibrates staking weight distribution. Our examination of the SRSW model demonstrates notable improvements in the decentralization metrics: the Gini index improves by 37.16% on average, while Nakamoto coefficients for liveness and safety see mean enhancements of 101.04% and 80.09%, respectively. This research is a pivotal step toward a more fair and equitable distribution of staking weight, advancing the decentralization in blockchain consensus mechanisms.

How Does Stake Distribution Influence Consensus? Analyzing Blockchain Decentralization

TL;DR

The paper tackles the problem of insufficient decentralization in PoS/DPoS blockchains due to weight concentration among validators. It formalizes decentralization metrics for weighted consensus, conducts an empirical study of ten permissionless blockchains, and introduces the Square Root Stake Weight (SRSW) mechanism to rebalance staking influence without adding new tokens. The results show substantial improvements in decentralization: the Gini index improves by on average, while Nakamoto coefficients for liveness and safety rise by and , respectively. This data-driven approach advances fairer stake distribution, enhances resilience against censorship, and reduces MEV risks, offering a practical path toward stronger decentralization in blockchain consensus.

Abstract

In the PoS blockchain landscape, the challenge of achieving full decentralization is often hindered by a disproportionate concentration of staked tokens among a few validators. This study analyses this challenge by first formalizing decentralization metrics for weighted consensus mechanisms. An empirical analysis across ten permissionless blockchains uncovers significant weight concentration among validators, underscoring the need for an equitable approach. To counter this, we introduce the Square Root Stake Weight (SRSW) model, which effectively recalibrates staking weight distribution. Our examination of the SRSW model demonstrates notable improvements in the decentralization metrics: the Gini index improves by 37.16% on average, while Nakamoto coefficients for liveness and safety see mean enhancements of 101.04% and 80.09%, respectively. This research is a pivotal step toward a more fair and equitable distribution of staking weight, advancing the decentralization in blockchain consensus mechanisms.
Paper Structure (25 sections, 3 theorems, 15 equations, 2 figures, 4 tables)

This paper contains 25 sections, 3 theorems, 15 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Consensus Mechanism Foundations and Classification
  3. Classification of Consensus Mechanisms Based on Finality
  4. Transition to Weighted Consensus
  5. Validator Set Selection
  6. Consensus Decentralization Metrics
  7. Validator Set Cardinality ($m$)
  8. Gini Coefficient ($G$)
  9. Nakamoto Coefficient - Liveness ($\mathbb{N}_L, \rho_{\mathbb{N}_L}$)
  10. Nakamoto Coefficient - Safety ($\mathbb{N}_S, \rho_{\mathbb{N}_S}$)
  11. Summary
  12. Empirical Data Analysis
  13. Scope and Methodology of Data Collection
  14. Data Analysis
  15. Advancing Decentralization: Finite SRSW Quorums
  16. ...and 10 more sections

Key Result

Theorem 1

Given a validator set $N$, the SRSW model's Nakamoto coefficient for liveness, $\rho_{\mathbb{N}_L}^*$, is greater than or equal to that of the linear stake-weight model, $\rho_{\mathbb{N}_L}$.

Figures (2)

  • Figure 1: Comparison of Nakamoto coefficients for safety and liveness in linear and SRSW weighting functions
  • Figure 2: Evaluation of SRSW against linear stake weight

Theorems & Definitions (7)

  • Definition 2.1
  • Definition 2.2
  • Theorem 1
  • proof
  • Theorem 2
  • Theorem 3
  • proof