To solve the doubts of the subject, you need to first understand the derivation process of introducing Leader (that is, the derivation process of multi-paxos), and clarify two concepts with the subject, basic-paxos (there is a livelock) and multi-paxos (introducing Leader).
We know that basic-paxos have a live lock and that it takes two stages to reach consensus. Because of these two limitations, we derive multi-paxos.
The reason for the live lock is that there are multiple proposers initiating proposals, causing multiple proposals to interfere with each other, so that no proposal can reach consensus in the end.
The simplest solution to this problem is naturally to introduce (not one) members of authority, i.e. Leader, and allow only members of authority to initiate proposals. Reducing the number of members who initiate proposals will naturally reduce the probability of proposals interfering with each other.
The Leader mentioned here is not the only strong Leader in the world, slightly different from the Leader understood by the subject, in multi-paxos allows the existence of multiple Leaders at the same time, if a strong Leader is introduced, there are indeed other algorithms that can be replaced, such as: Raft. So in multi-paxos, Leader is a collection, which is a subset of Proposer.
Because multiple Leaders exist at the same time, Leader is only to reduce the probability of livelocks, so it is not completely evasive to livelocks.
In addition, will the existence of multiple Leaders at the same time affect the correctness of the algorithm? No, as long as each Leader performs the consultation process in accordance with the preare → accept, the eventual correctness can still be guaranteed, because there will only be one majority with the highest proposal number, and other proposals with lower proposal numbers will not reach consensus.
With the introduction of Leader, we can quickly observe that the prepare phase is non-essential when there is no proposal interference (i.e., there is only one Leader).
Because the prepare phase is used to negotiate the proposal number, and the purpose of the negotiated proposal number is to gain ownership of the proposal number to initiate the proposal. When only one Leader A exists, no other member and that Leader A fight for ownership of the proposal originated, so Leader A can go straight to the accept phase and skip the prepare phase. When other Leader B take ownership of the next proposal number, then the accept stage of Leader A will not get the support of the majority, and thus re-enter the prepare stage.
And this is the multi-paxos negotiation process.