Law

Why 2f + 1

Even cluster sizes buy nothing: N = 4 tolerates one failure exactly as N = 3 does.

Q \leq N - f, 2 Q > N ⟹ N \geq 2 f + 1, Byzantine: N \geq 3 f + 1

Worked examples, recomputed

Every number the mechanisms quote for this relationship is recomputed from it, so none of them disagrees with it.

Each mechanism states it in its own names. The general symbol each name stands for is shown with it.

Distributed Systems Coordination
Who is allowed to decide, and how does everyone else learn the decision without asking?
$N \geq 2 f + 1$
Read it in place →
Distributed Systems Coordination
Who is allowed to decide, and how does everyone else learn the decision without asking?
$N \geq 3 f + 1$
Read it in place →