When does a quorum go strong?

Store each key on N replicas and you choose how many a read waits for (R) and how many a write waits for (W). The trade is the whole game: when R + W > NThe overlap rule: if the read quorum and the write quorum are big enough that they must share a replica, a read is guaranteed to see the latest acknowledged write. the two quorums are forced to overlap, so a read always sees the latest write — strong consistency. But every replica you add to a quorum is one more that has to be up for that operation to succeed, so bigger quorums buy consistency with availability.

The quorums
AcrossreplicasThe replication factor: how many copies of each key the system keeps. Reads and writes only ever need to reach a subset of them., a read waits forand a write forof them.
Each replica is up% of the time.
Write · 2
Read · 2
overlap — a read sees the writein the quorumoutside it
Strongconsistency

R + W = 4 beats N = 3 by 1 — the quorums overlap, so reads never go stale.

99.9997%reads availableThe chance a read can assemble its quorum: at least R of the N replicas are up. Bigger R means stronger reads but a lower chance the quorum is reachable.
99.9997%writes availableThe chance a write can assemble its quorum: at least W of the N replicas are up. W = N (write-all) is the most fragile write you can pick.
1failures survivedHow many replicas can be down at once while both reads and writes still work: min(N−R, N−W). Reads alone survive N−R losses, writes N−W.
R + W > NR + W = 4 beats N = 3, so every read quorum shares at least 1 replica with the latest write — a read can't miss it. And W clears half of N, so two conflicting writes can't both commit.
The trade-off, at N = 3
StrategyR / WReads upWrites up
Fast (R=1, W=1)eventual1 / 1100%100%
Majoritystrongyou2 / 299.9997%99.9997%
Read-one, write-allstrong1 / 3100%99.7%
Write-one, read-allstrong3 / 199.7%100%

Read down the two right columns: shrinking a quorum makes that operation more available, growing it makes the operation stronger but more fragile. Read-one, write-all gives the fastest, most available reads — and the most fragile writes; flip it for the mirror image. Majority quorums sit in the middle, the usual default. (Availability assumes replicas fail independently — correlated outages, like a shared rack or zone, hit several at once and erode these numbers.)

R + W > N ⇒ strong consistency · based on quorum consistency