[eloff]

Paxos solves a different consensus problem than PoW or PoS.

The former is for when you control and trust all nodes in your network. The latter is for the more difficult problem of consensus when you don't trust the nodes - otherwise known as the Byzantine Generals problem in distributed systems research.

[Vervious]

Pretty sure Paxos is easily extended to the byzantine setting with digital signatures (i.e. Byzantine Paxos has also been around forever). Also PBFT has been around since the 1980s.

Only distinction is classical consensus is permissioned whereas blockchains are typically permissionless.

[xtracto]

Exactly. And paxos is not the best algorithm at it. There is Raft which is an alternative that is easier to understand.

[tlamponi]

Best in what metric?

raft and paxos are basically the same, besides leader election, which raft's take makes it simply easier and possible even more efficient[0]. I say "possible" because that depends very much on the consensus state over time, which in most actual workloads can be pretty stable, so at least in some practice, e.g., with hypervisor-cluster like we do, they perform almost the same. The simpler approach of raft can help if you create a library for it from scratch, or for easier understanding when coming into that space, otherwise the differences does not matter too much (in practice), IMO.

[0]: https://arxiv.org/abs/2004.05074

[eloff]

I gather OP means best because it's understandable and easier to implement. Paxos has a tough reputation and even Google fucked it up in the beginning according to their Chubby distributed lock paper.