Social Consensus, Nakamoto Consensus

1 [general]
Agreement among the majority of nodes as to which block or blockchain to follow
2 [social consensus]
Agreement among the community and developers over which direction the protocol should be developed, and how miners should choose to include transactions. This is often aligned with Miner/Nakamoto Consensus, but at times can differ.
3 [nakamoto consensus]
One of the core rules which make Proof of Work (PoW) chains work and give them security. Nakamoto Consensus is a rule where miners follow the chain with the most accumulated Proof of Work (PoW) at any given moment, on a given ruleset.

This simple idea allows the blockchain to function in a decentralized, trustless way as it provides incentivize for miners to cooperate and act honestly; building upon the same ledger as the rest of the network.

Miners come across this situation commonly in two situations.

3.1 Example | Double spend attempt

A miner tries to mine a double spend transaction in a block against the rest of the network. Unless the miner is able to accumulate more proof of work than the entirety of the network combined, the honest chain will grow quicker than the dishonest way, forcing the miner to continue wasting resources, or to join the longest chain and act honestly, indirectly punishing the dishonest miner for going against Nakamoto Consensus.

3.2 Example | Orphan blocks

Sometimes multiple miners discover a block so close to each other they are each able to propagate their block to a part of the network. Each node will use the block they received first as the valid one and begin building upon that one, causing a temporary fork. Once a second block is found the miners will see that longer chain and recognize it as being the one with the most Proof of Work (PoW) resulting in any miners working on the alternative fork to move over and continue building on the longest chain.