Quorum or $B$qrm
It's easy to mistake the most common form for quorum; which is nodes length / 2 + 1 is about a majority of nodes agreeing with each other because that's how things are usually decided in government or in groups. But it's that's not true necessity for a quorum. A quorum is a required threshold of nodes, such that any group meeting that threshold will intersect with any other such group. This means in as plain english as it is possible, it is a class of possible sets, not a single concrete set. Such rules for construction are decided by the Implementation. It is a critical concept in distributed systems to ensure that decisions cannot contradict previously chosen values.
To maintain B2, a ballot’s quorum was chosen to contain a µαδζ∂ωριτ˘ιστ of priests. Initially, µαδζ∂ωριτ˘ιστ just meant a simple majority. Later, it was observed that fat priests were less mobile and spent more time in the Chamber than thin ones, so a µαδζ∂ωριτ˘ιστ was taken to mean any set of priests whose total weight was more than half the total weight of all priests, rather than a simple majority of the priests. When a group of thin priests complained that this was unfair, actual weights were replaced with symbolic weights based on a priest’s attendance record. The primary requirement for a µαδζ∂ωριτ˘ιστ was that any two sets containing µαδζ∂ωριτ˘ιστ of priests had at least one priest in common. To maintain B2, the priest initiating a ballot B chose Bqrm to be a majority set.LAMPORT, P. 9 — §2.2
First fatphobia, and just general. eww. But the last sentence is the vital one. Lets think about three nodes. A, B, and C. We want to ensure that any two quorums have at least one node in common. If we pick a majority set, then we are guaranteed that any two sets will have at least one node in common. This is because if we have a set of 2 nodes out of 3, then any other set of 2 nodes will always have at least one node in common with the first set. This is the vital requirement for maintaining B2 in Paxos. If a quorum of nodes are queried in a future about a decree we can be sure one of them will have seen the associated value. There are other less used examples of quorum such as weighted nodes but for the paper we will assume it to be the simple form.
