quorums

Quorum is the minimum number of members of a group that must be present or in agreement to conduct business or make changes. In governance and voting, a quorum ensures decisions are representative and prevents actions by too small a subset.

In distributed systems, a quorum is the minimum number of nodes that must participate in a decision, such as committing a write or validating a value. With N replicas, a simple majority is floor(N/2) + 1. The use of a quorum allows systems to tolerate up to f failed nodes (crashes) while still making progress.

Read and write quorums: to preserve consistency, many systems require a write quorum W and a read quorum R such that R + W > N, ensuring that a read reflecting the most recent write can be served from the intersection of quorums.

Quorum systems and safety: a quorum system is a collection of quorum sets with the property that any two quorums intersect. This guarantees that a decision endorsed by one quorum can be observed by any other quorum, ensuring safety as long as enough nodes are functioning. In practice, different systems tune quorum sizes to balance availability and consistency.

Variations: crash-fault quorums tolerate non-Byzantine failures; Byzantine quorums tolerate arbitrary malicious behavior and require larger quorums and sometimes specialized protocols (for example, Byzantine fault-tolerant consensus) to guarantee safety and liveness. In practice, systems such as Paxos, Raft, and Cassandra use quorum-based approaches to achieve reliable progress in the presence of failures.