What is the Nakamoto Coefficient and the Superminority
The Nakamoto coefficient measures the smallest coalition of independent actors capable of disrupting network consensus. In proof-of-stake networks, where 33.4% of staked tokens is sufficient to prevent the chain from finalizing, that specific set is referred to as the superminority. The metric serves as a decentralization gauge: a lower coefficient indicates a network can be shut down by a relatively small group, whereas a higher coefficient implies it would take a massive collective effort to interrupt the system.
We can think of this threshold using a jury analogy. A conviction verdict is only possible when all 12 jurors agree. A single dissenting juror is powerless to force an acquittal, yet is equally unable to stop a conviction, and can ultimately cause a mistrial. This mirrors proof-of-stake protocols: 33% of a network's validators could not alter the state of the blockchain, but if that percentage refuses to participate, they freeze the entire network. The Nakamoto coefficient simply quantifies how many jurors would need to agree to bring down a blockchain.
How Solana Measures Its Coefficient
To calculate the coefficient for Solana, we list each validator, rank them by their token amount held, and then calculate a running total of their stake. The Nakamoto Coefficient is simply the number of validators in that running total needed to reach 33.4%. For the past year and a half, Solana has sat at around 20. This means that of the many thousands of validators on the network, any 20 of them combined together would be able to disrupt Solana. Dashboards like Solana Compass show the coefficient in real-time. Anyone can see who these superminorities are.
Why is the disruption line 33.4%, rather than 51%? Consensus protocols like Solana's rely on what is known as Byzantine fault tolerant (BFT) consensus. In BFT consensus networks, consensus is guaranteed as long as less than 1/3 of the network is maliciously voting out of line. The system fails to reach consensus if the total amount of stake that is actively working against the system exceeds 1/3 of the network stake. If the superminority is able to vote in a way that causes disagreement, they will effectively shut down the network because the remaining 2/3 of the validators will be unable to reach consensus. Note that these validators will not be able to steal user funds, nor can they forge signatures. The only thing they would do is to prevent the network from functioning.
How Ethereum and Bitcoin Stack Up Against Solana
It is important to note that comparing Solana's coefficient against other proof-of-stake protocols and against Bitcoin isn't apples-to-apples, as you are measuring completely different kinds of organizations. Some proof-of-stake protocols on the Cosmos blockchain have had coefficients of less than ten validators. Ethereum has hundreds of thousands of "validator keys", but many of these are controlled by the same organization. Lido, the leading liquid-staking protocol, currently accounts for almost 30% of all staked ETH on Ethereum.
Bitcoin, in its own way, has a coefficient of only about 3-4. Bitcoin miners can organize into pools to increase the profitability of their operation, and the largest pool in terms of mining hashrate has, for a time, controlled more than half of all hashrate. Solana's coefficient of 20+ isn't a "10x better than Bitcoin" kind of deal. Rather, 20+ validators is decent. It is better than other proof-of-stake validators in existence today. However, unlike in a Bitcoin network, one of these entities on Solana could in theory account for 50% of the whole network.
Why the Nakamoto Coefficient Matters
Given that it is the most useful and widely cited figure in the decentralization discussion around Solana, it is important to acknowledge the shortcomings of the coefficient. The figure only takes into account stakeholders. Many of these validators are renting server space from a handful of infrastructure providers, which means that the number of stakeholders controlling more than 33% of the network is in fact much smaller. For example, there were two data center power outages at Equinix and OVH in 2022 that knocked out dozens of validators. There is also no guarantee that the 100+ validators on Solana represent enough diversity across legal jurisdictions. The Nakamoto coefficient is helpful in providing insight into who is running Solana and the degree of centralization, but it isn't the be-all-end-all of what decentralization should look like.
In practical terms, let's imagine you are a Solana DeFi whale considering moving a large lending position from Ethereum to a lending protocol on Solana like Kamino. You hear a claim that Solana is effectively centralized by a small group. You don't have any way to verify it yourself, so you consult a trusted friend with the relevant technical knowledge. They point out that you would need roughly 20+ operators coordinating together to shut down Solana, whereas Ethereum had one protocol that alone had nearly 33% of stake, which is exactly the threshold to stop the chain. Your friend also points out, however, that many of these operators use servers from a handful of cloud services providers, so their decentralized infrastructure isn't what it might initially appear. While the argument won't be settled by the coefficient, it will be converted into a debate over the facts.
Can the superminority steal funds?
No. In the same way that the 12th juror can not vote a conviction, the superminority could not be used to alter the state of the Solana chain. This includes forging signatures or taking funds from user accounts. The only thing the superminority can prevent from being broadcast across the network is a new transaction being signed by the user's private key.
