A quorum is a subset of participants large enough that the protocol can rely on its overlap with other quorums.

For $N$ participants, any two strict majorities contain at least one participant in common. That intersection is useful because information accepted by one majority cannot be completely disjoint from a later majority.

Replicated stores often express the same idea with a write quorum $W$ and read quorum $R$. If

$$R+W>N,$$

then every read quorum overlaps every write quorum. If

$$2W>N,$$

then any two write quorums overlap.

Quorum intersection does not by itself determine which value is correct or newest. A protocol still needs rules for versions, terms or committed state.

The same intersection principle appears in replicated storage, leader election and consensus protocols.