Reliable consensus is impossible once a third or more of participants may behave arbitrarily.
Lamport, Shostak and Pease proved in 1982 that consensus requires more than two-thirds honest participants. The result underlies classical Byzantine-fault-tolerant consensus protocols and influenced later distributed-ledger designs, though not every blockchain relies on this exact fault model or threshold.
In practice
- Three of ten regional offices report figures that cannot all be true, and headquarters must decide what the company's number is without knowing which offices are wrong.
- A distributed team with unreliable messaging cannot agree a release time if any member may be silently offline or mistaken.