This is a classic technical problem, and there have been a lot of research results in both academia and industry (including Paxos, Byzantine series algorithms, etc.).
The core of the problem is how to solve a certain change to obtain a consistent execution result in the distributed network, which is recognized by all parties involved, and this information is determined and irreversible.
The requirements of this problem are quite different in the public anonymity scenario and the permission management scenario, which leads to two types of ideas: probability-based algorithms and deterministic algorithms.
Originally, the Bitcoin blockchain considered worst-case guarantees in the context of public anonymity. By introducing the "Proof of Work" strategy, the malicious behavior of a small number of people is avoided, and the probability model is used to ensure that the last participating parties agree to the longest chain. The core idea of the algorithm is a game based on economic interests, so that participants
who will lose economic interests, thus ensuring the cooperation of most people. At the same time, confirmation must be achieved after the generation of multiple blocks, which is guaranteed probabilistically. The main problem with this type of algorithm is its inefficiency. Similar algorithms include PoS, DPoS, and Casper with equity as collateral.
Later, more blockchain technologies (such as Hyperledger) began to consider supporting more deterministic consensus mechanisms in scenarios with permission management, including classic Byzantine algorithms, which can solve the problem of rapid confirmation.
The consensus problem will be a research hotspot of great academic value for a long time, and the core indicators will include the proportion of fault-tolerant nodes, decision convergence speed, recovery after errors, and dynamic characteristics. Probability-based algorithms such as PoW theoretically allow less than half of non-cooperative nodes, and deterministic algorithms such as PBFT
theoretically allow no more than 1/3 of non-cooperative nodes.