Agreement without talking to everyone
In a replicated system you do not need every replica to respond, only enough to guarantee overlap. A quorum is the minimum number of nodes that must participate in an operation. By choosing quorums that always overlap, you ensure a read sees the latest write.
The overlap rule
Let there be N replicas. A write must reach W of them and a read must consult R of them. The key constraint is that reads and writes must share at least one node.
- The rule is W plus R greater than N.
- That overlap means any read quorum includes a node that saw the latest write.
- Larger W gives durable writes, larger R gives fresh reads, and they trade off.
If W plus R is not greater than N, a read quorum can entirely miss the nodes that took the last write, returning stale data.
A concrete setting
With five replicas, choosing W of three and R of three guarantees overlap, since three plus three exceeds five. Any read of three nodes must touch at least one of the three nodes that accepted the write.
Key idea
Quorum based decisions require that the write set and read set overlap, captured by W plus R greater than N, so every read is guaranteed to see at least one node holding the most recent write.