About Quorum
In a certain Quorum, the honest nodes reached a consensus<=>The honest nodes in the entire network also reached the same consensus.
How to calculate the size of Quorum:
Every honest node of Quorum needs to reach a consensus. According to the concept that the minority obeys the majority, so |Q| must be an odd number.
Each Quorum's honest node has reached a consensus, but there is no guarantee that each Quorum's honest node has reached the same consensus. If the same consensus is required, there needs to be an intersection of honest nodes in every two Quorums. At this time, it can be guaranteed that the consensus reached by the honest nodes in the two Quorums is the same.
For the Byzantine problem
Security: For the Byzantine general problem, the intersection of two Quorums needs to be greater than or equal to f+1 to ensure that there is an honest node in the intersection. Therefore, the size of the intersection is 2Q-N>=f+1 (equivalent to 2Q-N>f).
Activity: Q is to be composed, so many people from Q need to express their opinions. We know that bad people may not express their opinions, so Q<=N-f
Judgment: There may be malicious nodes in Q. If Q is not an odd number, then the malicious nodes will interfere with Q to reach a consensus.
N+f<2Q<=2(N-f)=>N>3f
N=3f+1, when Q takes 2f+1, the inequality can be satisfied~