Consensus Mechanism
The rule set that lets many independent computers agree on one shared history without trusting each other.
A consensus mechanism does two jobs. First it decides who may propose the next block in a way that cannot be gamed by creating fake identities, which proof of work solves with expenditure on computation and proof of stake solves with capital at risk. Second it defines a fork-choice rule that tells every node which chain to follow when two valid candidates exist, whether that is the chain with the most accumulated work, the one with the most attested stake, or the output of a voting round in a Byzantine fault tolerant protocol. Every such mechanism rests on an assumption about how much of the network is honest, commonly a majority of work or stake, or two thirds in BFT designs, and its guarantees fail if that assumption fails.
In practice
Tendermint-style chains run a voting round for each block, so a block is agreed and final within one round rather than becoming steadily harder to reverse.
The common misunderstanding
Consensus is about agreeing on the order and validity of transactions, not about voting on whether a transaction is desirable or fair.