The concept of consensus is straightforward: consensus is when the network agrees on what information stored in the network is true and should be kept, and what is not true and should not be kept. For Bitcoin, achieving consensus is a simple matter of coming to agreement on the set to send and receive of Bitcoin across the network. For other networks, achieving consensus would also involve coming to an agreement on the final state of smart contracts, medical records, or any other network information stored on the blockchain.
Consensus algorithms have been the subject of research for decades. The consensus algorithms for distributed systems have to be resilient to multiple types of failures and issues, such as corrupt messages, parts of a network connecting and disconnecting, delays, and so on. In financial systems, and especially in blockchains, there is a risk of selfish and malicious actors in the system seeking profit. For each algorithm in a blockchain network...