Quorum Arithmetic — Why R + W > N
The one inequality that makes quorums tunable
With N replicas, a write acked by W and a read from R:
If R + W > N, the read set and write set must overlap on at least one replica — so every read sees the latest acknowledged write. That overlap is strong consistency. And W > N/2 stops two concurrent writes both reaching quorum (no split-brain).
Try every R/W setting
Flip between quorum configs (balanced, fast, eventual, read-optimized) and predict whether a worst-case read is guaranteed to see the latest write. The rule R+W>N is the pigeonhole made visual — the read and write quorums must share a node.
Tuning (N=3)
| W | R | R+W>N? | Behaviour |
|---|---|---|---|
| 3 | 1 | ✓ | Fast reads, slow/fragile writes |
| 1 | 3 | ✓ | Fast writes, slow reads |
| 2 | 2 | ✓ | Balanced strong consistency (common default) |
| 1 | 1 | ✗ | Fastest/most-available, but eventually consistent |
Bigger W = stronger durability, slower writes; bigger R = fresher, slower reads. R=W=1 (R+W≤N) = max speed/availability, eventual consistency — Dynamo-style. Sloppy quorum + hinted handoff writes to the next available node when a target is down, trading strict membership for availability.
Takeaways
- R + W > N ⇒ strong consistency; W > N/2 ⇒ no split-brain.
- Tuning (W,R) dials the consistency–latency trade-off per operation.
- Raft’s commit is just a write quorum (majority ack).
Re-authored from-scratch; diagram hand-authored (SVG) for this guide.
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