What is the Nakamoto Coefficient?

As the wave of adoption in decentralized blockchains continues, it is important we pay attention to how decentralized these blockchains are. One metric to gauge the decentralized nature of a blockchain would be the Nakamoto Coefficient. The Nakamoto Coefficient represents the number of validators (nodes) that would have to collude together to successfully slow down or block any respective blockchain from functioning properly. The higher the Nakamoto Coefficient relative to the total number of validators, the lower the risk of collusion disrupting a decentralized blockchain.

Byzantine Fault Tolerance

Think about Bitcoin’s Byzantine Fault Tolerance design, where 51% of the validators would have to be in agreement in order to make changes to the chain. With just about 14,409 nodes in the Bitcoin Network, according to bitnodes.io, it would take a Nakamoto Coefficient of 7,349 validators to slow down the network. For other blockchains, there are different byzantine fault tolerance designs, and usually less validators.

Let’s take a look at the Nakamoto Coefficient for some of the most popular blockchains.


(Author’s Note:while we have provided a chart below, it is important to note that blockchain teams often have dedicated resources to ensure they are one of the top validators of their network. A proportionally higher amount of voting power may come from internal validators present in these systems. This may skew the Nakamoto Coefficient to look like only a few nefarious validators are needed to disrupt the network from functioning properly, but in reality, a much higher amount of validation power would be needed to do so.)

BlockchainNakamoto CoefficientTotal # of Validators
Bitcoin7,34914,409
Avalanche261,188
Binance Smart Chain744
Cosmos6150
Fantom366
Polygon2100
Solana191,249
Terra7130
THORChain1037

Budding Blockchains

As you can see, many budding blockchains may be susceptible to coordination between only a few validators within their system. This is understandable for their early stages. A blockchain’s growth happens naturally, but a rigorous attention to decentralization should be front and center. Understanding the incentive structure of validators is important too. It will never be economically feasible to buy enough computing power to disrupt the network that you own a massive percentage of.

FAQ:

Why is Ethereum not included in the above chart?

Because of the large network size of Ethereum, the total number of validators is undetermined.

Is the Nakamoto Coefficient the only metric to gauge the decentralized nature of a blockchain?

No, there are other metrics that may help gauge the decentralized nature of a blockchain. 

Let’s take into account the analysis of Balaji S. Srinivasan and Leland Lee in Quantifying Decentralization. The Lorenz curve and the Gini coefficient are two tools for measuring the non-uniformity within a population. The Lorenz curve is generally a mathematical function estimated from an incomplete set of observations. From the area under the Lorenz curve is where the Gini coefficient is calculated. The closer the Gini coefficient is to zero, the more uniform the distribution of resources. When the distribution of resources is more skewed to one party, the closer the Gini coefficient is to one. 

When G=1, there is one decision maker to capture to compromise the system. When G=0, there are multiple decision makers needed to be captured to compromise the system. This means that a low Gini coefficient equals a high degree of decentralization.

Image for reference:

Source: https://coinmarketcap.com/ from: https://news.earn.com/quantifying-decentralization-e39db233c28e

It is important to note the difference between a decentralized system and a decentralized subsystem. The calculation is dependent on the chosen subsystems. If you were to choose an alternate subsystem, the measure of decentralization would be different. For example, Bitcoin is a decentralized system composed of decentralized subsystems.

We will use these six subsystems to illustrate how to measure the decentralization of Bitcoin or Ethereum. Please note: you may decide to use different subsystems based on which ones you consider essential to decentralization of the system as a whole. (Source: https://news.earn.com/quantifying-decentralization-e39db233c28e )

While the Gini Coefficient is another metric for measuring the level of blockchain decentralization, the 0-1 scale restricts the data because it is not a direct representation of the number of entities required to compromise a system. That is why the Nakamoto Coefficient is an additional approach to configuration. The Nakamoto coefficient is based on the Lorenz curve, from which the Gini Coefficient is calculated.

Conclusion

The Nakamoto Coefficient is just the beginning of measuring the numerics of decentralization. With little information, we are able to start crediting changes in decentralization to individual deployment of code or network activities. With the limited resources we currently have, we are already able to detect either the need for deployment or for additional client developers in order to improve decentralization of a blockchain. The overall goal is to optimize decentralization, and it is necessary to begin with quantitative metrics such as the Lorenz curve, the Gini coefficient, and the Nakamoto coefficient. It is important not to look at the Nakamoto coefficient as the finish line, but as the start to a great race.

Sources:

explorer.avax.network/validators

https://solanabeach.io/validators

https://thorchain.net/#/nodes

https://bscscan.com/validators

https://stake.id/#/

https://ftmscan.com/validators

https://www.mintscan.io/cosmos/validators

https://bitnodes.io/

The opinions expressed in the CrossTower Classroom are those of the author(s) and not necessarily that of CrossTower. We appreciate diverse perspectives of our employees and we thank them for having a voice. 

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CrossTower Inc. provides this content for general information purposes, to better inform you on your digital asset investment journey. We do not provide investment recommendations or provide tax advice. Please consult your investment professional or tax advisor if you require assistance in these areas.

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