Archivedistributed-systems
Quorum Math: Why Odd Numbers and Majority Rules
R + W > N gives consistency; majority quorums give availability under f failures. The rest is arithmetic.
- Published
- Reading time
- 1 min read
For N replicas with read quorum R and write quorum W, a read is guaranteed to see the latest write when R + W > N. With N = 3, R = W = 2 works; R = 1, W = 1 does not.
Failure tolerance
A majority quorum floor(N/2) + 1 tolerates floor((N-1)/2) failures. That is why clusters use 3, 5, or 7 nodes: 3 tolerates 1, 5 tolerates 2. Even-sized clusters tolerate the same failures as the odd size below them while costing more, hence odd numbers.
The subtleties
- Quorum intersection ≠ freshness in asynchronous systems. A read quorum can miss an in-flight write that has not committed.
- Sloppy quorums (Dynamo-style hinted handoff) improve availability and weaken the guarantee.
- Reconfiguration changes
N; quorums must be computed for the current configuration, and joint consensus or single-node changes are needed to avoid split brains.
Takeaway: quorum arithmetic tells you when replicas overlap, not when data is fresh. Pair it with a consistency protocol and read repair.