Background
There has been substantial discussion about the level of geographical decentralisation, both in Lido
research forums and in the more general Ethereum research forums. The reason behind such
concerns is the possibility of some legislation to try to ban blockchain, as has occurred with
cryptocurrency mining in the past. But beyond regional jurisdiction, other parallels, like cloud
providers and software centralization, also have inherent risks that should be avoided. Simon Brown
(Consensys) has been looking into these risks and wrote an interesting article with a first analysis of
Ethereum’s contemporary level of centralisation. This article caught Vitalik’s attention, and he
provided some feedback on novel statistical tools that could be used to extend the previous work.
This project builds on top of the previous work as a collaboration between MigaLabs and
Consensys, and with support and feedback from Vitalik, to use new datasets and new mathematical
tools to get a better idea of the level of (de) centralisation of the Ethereum’s staking node operators.
Problem Statement
We want to measure the level of (de) centralisation in the Ethereum validator set by calculating the
market concentration of node operators, adjusted for how correlated they are to each other. The
reason for this is that even if we have thousands of different node operators, each with a relatively
equal market share (under 1%), there could still be a relatively high risk of centralisation if they are
all based in the US, all using AWS, and all using the same client software. Measuring the market
share alone doesn’t reflect this nuance and can result in a “false positive” regarding the effective
level of decentralization in the network.
Approach
Initially, we will start by just calculating the market concentration of node operators. To do this, we
use the Herfindahl–Hirschman Index (HHI) to measure market concentration based on the market
share of each node operator. We then re-calculate the HHI after adjusting the market share of each
node operator by applying a correlation coefficient. The correlation coefficient for a node operator iscalculated from the sum of each node’s correlation scores under the operator’s control. This gives us
a single index based on the market share for each node operator, adjusted for how correlated they
are to each other in terms of geographical location (legislation), cloud provider, client software used,
and MEV relays. This index number tells how truly concentrated or decentralized the network is.
Deliverable
MigaLabs will work on this project with @orbmis (Consensys), and we will deliver a full research
paper explaining the methodology used, including the datasets used for the research, the
mathematical tools used, the implementation of the data analysis, and our conclusions. The
objective is to publish this article in arXiv for the community to access it easily and submit it to an
internationally renowned conference. Additionally, we can present the results of this research in one
of the Lido node operator’s calls.
Resources
For this project, we are asking for a timeline of three months and DAI$16,000 from Lido paid to the address 0x492d683a51613aBcef3AD233149d69b7FE60FBd7. LEGO will
be part of the paper’s acknowledgements in the arXiv version and at the conference.
This is a super interesting study to do especially since EL decentralization is a key topic these days, and LEGO has happily approved this grant request.
Just for full transparency: as I am a researcher at Consensys, the cost of my time is covered by Consensys, thus this Lido disbursement is to support the Miga Labs’ part of the work.
Hey @leobago thank you for this proposal and looking forward to the results of it!
The grant was disbursed - Ethereum Transaction Hash (Txhash) Details | Etherscan
Very interested to see this paper.
Hi all
Thank you very much for your interest, I am happy to report that the paper has been published and is available here: [2404.02164] Exploring Correlation Patterns in the Ethereum Validator Network
Hope you enjoying reading as much as we enjoyed working on it. 
Thanks!
Leo
Very interesting results, tank you for sharing Leo!
Would love to have you on one of the future Node Operator Community Calls to present!