Author: Deep Tide TechFlow

In the cryptocurrency space, Ethereum has become a focal point.

Decentralization is not only Ethereum's core promise but also a major source of its appeal. However, with Ethereum's upgrades and developments, the community has begun to question its true level of decentralization.

These concerns are not unfounded; we often see scattered posts discussing "Ethereum becoming centralized" from different perspectives.

Decentralization involves not only the dispersion of power and control but also the network's resistance to censorship, security, and transparency. Therefore, understanding the degree of decentralization in Ethereum is crucial for investors, developers, and ordinary users.

To address these concerns, Simon Brown, a researcher at Consensys, the parent company of MetaMask, decided to conduct an in-depth study using a more rational, rigorous, and systematic approach, employing various indicators and models for academic analysis, aiming to reveal the true state of decentralization on Ethereum.

To facilitate understanding of the key arguments, Deep Tide Research Institute has interpreted and organized the original paper.

Original Paper "Measuring the Concentration of Control in Contemporary Ethereum"

## I. Methodology: How to Measure the Degree of Decentralization in Ethereum?

Decentralization is a complex concept that involves multiple dimensions and angles. To accurately measure the degree of decentralization in Ethereum, the author of this paper, Simon Brown, employed various statistical methods and indicators for comprehensive measurement.

First, he introduced the Gini index, a statistical measure of inequality commonly used in wealth distribution statistics.

Here, it is used to measure the distribution of resources or power within the network. The Gini index ranges from 0 to 1, where 0 indicates complete equality and 1 indicates complete inequality. For example, a Gini index value of 0.9 means that resources or power in the network are highly concentrated.

In addition to the Gini index, researchers also considered: HHI (Herfindahl-Hirschman Index): typically used to measure the level of competition in specific industry sectors;

Shannon Index: sensitive to the size of the distribution in the data and the diversity of different values within the distribution, thus highlighting differences in distribution that the Gini index may not capture.

Atkinson Index: based on social welfare methods, inferring how much resource redistribution is needed to achieve a certain level of equality.

Jensen-Shannon Divergence: since we are interested in the decentralization level changing over time, this method is used to measure the similarity or difference between two probability distributions (Deep Tide Note: Simply put, it assesses whether the degree of centralization in Ethereum is similar or significantly different before and after a certain point in time).

Nakamoto Coefficient: a measure of the resources or power controlled by the largest n entities in the system. For example, if the top 5 entities control more than 50% of the resources, the Nakamoto coefficient is 5. This provides an intuitive sense of the influence of major entities in the network.

The selection of these indicators and models is not arbitrary. They have been carefully chosen to ensure that various aspects of decentralization are captured from different angles. This multi-faceted approach ensures the comprehensiveness and accuracy of the results, helping researchers better understand the true state of Ethereum's decentralization.

## II. Research Subjects: Which Indicators to Represent the Degree of Decentralization in Ethereum?

To delve into the degree of decentralization in Ethereum, it is first necessary to select appropriate data and subjects that can represent various important aspects of the Ethereum network and provide meaningful metrics for decentralization.

With Ethereum's transition to POS and the emergence of new technologies such as MEV and account abstraction, this paper considers various aspects and processes involved in an Ethereum exchange and summarizes the following suitable indicators to measure the degree of decentralization in Ethereum:

• Based on the Original Nakamoto Coefficient:

• Consensus nodes by client

• Consensus nodes by country

• Execution nodes by client

• Execution nodes by country

• Distribution of native asset by amount

• Amount staked by pool/staking service provider

• Indicators Related to PBS:

• PBS refers to the blocks proposed by builders and relayers, which play a key role in the Ethereum network.

• Blocks proposed by builder

• Blocks proposed by relay

• Indicators Related to Account Abstraction:

• Number of user operations per bundler

• Number of wallets per deployer

• Other Indicators:

• Effective inflation rate adjusted for burn

• Percentage of total supply staked

• Layer 2 rollups by relative TVL

Different indicators are also assigned different weights.

## III. Results and Interpretation: How Decentralized is Ethereum?

The researchers conducted a 90-day observation of Ethereum from May 23, 2023, to August 23, 2023. The overall research goal was to explore how the dynamic characteristic of decentralization changes over time within Ethereum, rather than being a static quality that remains balanced.

### A. Discussion of Results

From the data below, it can be seen that when the research model is applied to the same data, different indices yield different results. Taking the Gini coefficient as an example:

• Execution nodes by country: Gini index of 0.85

• Execution nodes by client: Gini index of 0.74

• Consensus nodes by country: Gini index of 0.79

• Consensus nodes by client: Gini index of 0.57

• Distribution of native asset: Gini index of 0.91

• Amount staked by pool/staking service provider: Gini index of 0.76

• Blocks proposed by builder: Gini index of 0.78

• Blocks proposed by relay: Gini index of 0.54

• Number of user operations per bundler: Gini index of 0.13

• Number of wallets per deployer: Gini index of 0.03

• Layer 2 rollups by relative TVL: Gini index of 0.87

The color coding of these values is for ease of reading; the closer the color is to red, the higher the concentration, and the closer it is to green, the higher the degree of decentralization.

It is evident that the degree of centralization in Ethereum is very high for the indicators of stablecoins and staking pools. This seems to correspond with the high market shares of USDC and USDT in reality, as well as LDO's leading position in the liquid staking space.

### B. Results Based on Original Nakamoto Coefficient Subsystem Selection

Network Nodes: When researchers examined the data related to the measurement dimensions based on the original Nakamoto coefficient subsystem, they first applied the Gini index to the indicators related to network nodes (Deep Tide Note: The Nakamoto coefficient measures the resources or power controlled by the largest n entities in the system).

From these analyses, we can observe that both "execution nodes by country" and "consensus nodes by country" maintained relatively high Gini index values of 0.85 and 0.79, respectively. This indicates that these consensus nodes and execution nodes are highly concentrated in certain countries.

### C. Indicators Related to PBS

PBS refers to the blocks proposed by builders and relayers. The data shows that between the first and last 24-hour intervals of the dataset, the number of blocks proposed by a single builder and relayer, as well as the overall concentration in the market, underwent significant changes. This indicates that the degree of decentralization in the Ethereum network increased during this period.

### D. Other Indicators

When we examine the Rollups by TVL, we observe a noticeable level of centralization, with a 90-day average Gini index value of 0.87. These values are meaningful when observing the underlying data, where a single rollup (Arbitrum One) holds 54.3% of the TVL among all rollups (down from 64.5% at the start of the sample). The second is Optimism, with a TVL of 25.9%. This means that despite the existence of multiple rollups, two of them dominate the majority of the market share.

### E. Indicators Related to Account Abstraction

This section of the data primarily focuses on the impact of ERC-4337 bundlers. The data shows:

• The 90-day Gini index for User Operations by Bundler ranges from 0 to 1, with a median of 0.6 and a standard deviation of 0.36.

• A specific bundler holds 76% of the market share among 13 active bundlers.

This data indicates that the account abstraction space is still in its early stages, and the infrastructure has not yet seen significant maturity or adoption. The impact of ERC-4337 bundlers on the network's degree of decentralization is relatively limited, so a moderate level of centralization is acceptable.

### F. Main Index Reveals Overall Increase in Centralization

The main index provides us with a high-level metric to measure how the degree of decentralization in the entire network changes over time (2023/05/23 - 08/17).

The Gini index decreased from 21% to 14% across all measurement dimensions, while the HHI index slightly increased from 7.5% to 10%.

• Significance:

• The decrease in the Gini index indicates an increase in the degree of decentralization or a decrease in concentration.

• The increase in the HHI index indicates an increase in concentration.

• Conclusion: Taking both indices into account, we can say that overall, the degree of decentralization in the Ethereum network increased during this period.

## IV. Overall Conclusion and Future Outlook

Through in-depth research and data analysis, the researchers have drawn the following conclusions regarding the degree of decentralization in Ethereum:

• The degree of decentralization in Ethereum is dynamic: Rather than being a static quality that remains balanced, decentralization is a dynamic characteristic that changes over time. This means that as the Ethereum ecosystem develops and evolves, its degree of decentralization will also change accordingly.

• Different measurement dimensions show different levels of concentration: For example, the classification of execution nodes and consensus nodes by country and client shows varying levels of concentration. This emphasizes the importance of using multiple methods to measure decentralization.

• Certain areas show high levels of centralization: For instance, in the Rollups by TVL, Arbitrum One and Optimism hold the majority of market share, indicating significant centralization.

• Ongoing efforts are needed to maintain decentralization: The research results clearly indicate that the entire Ethereum ecosystem shows elements of concentrated control, which may be much less than the community expects. This means that continuous efforts are needed to maintain a healthy degree of decentralization.

Future Outlook

As the Ethereum ecosystem continues to evolve, its components and overall infrastructure will also change. This means that to ensure Ethereum's decentralization, the community needs to continuously monitor and assess its degree of decentralization and take necessary measures to ensure its health and stability.

Moreover, with the emergence of new technologies and solutions, new measurement dimensions and methods may be added to the assessment of decentralization. This requires researchers to continually update and refine their models to ensure their accuracy and relevance.

Overall, decentralization is not only a technical challenge but also a shared responsibility of the community and ecosystem. Only through ongoing efforts and collaboration can we ensure Ethereum's decentralization and its long-term success.