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The minimum number that breaks any network
The Nakamoto Coefficient answers: “How many independently operated entities would need to collude to compromise the network?” For each property — consensus, block production, node policy — you rank entities by share and count until the cumulative total exceeds the threshold (typically one-third for consensus sabotage).
- High coefficient (e.g. 10+) — no small club can censor you; robust.
- Low coefficient (e.g. 3) — a handful of actors hold the keys to the network.
Where the thresholds come from
In proof-of-work it is modeled on the classic Byzantine fault tolerance bound: one-third of malicious miners can disrupt liveness; more than half rewrites history. The same math, translated into staked capital for proof-of-stake networks.
Watch out: a high coefficient on consensus says nothing about governance. A chain can be miner-diverse but still run by one foundation that upgrades it. Read all four pillars together.