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Consensus mechanisms in blockchain applications allow mistrusting peers to agree on the global state of the chain. Most of the existing consensus mechanisms, however, are constrained by low efficiency and high energy consumption. In this paper, we propose the Blockchain Reputation-Based Consensus (BRBC) mechanism in which a node must have the reputation score higher than a given network trust threshold before being allowed to insert a new block in the chain. A randomly-selected set of judges monitors the behaviour of each node involved in the consensus and updates the node reputation score. Every cooperative behaviour results in a reward, and a non-cooperative or malicious behaviour results in a punishment. BRBC also uses the reputation score to revoke access to nodes with a reputation score below a given threshold. We present a security analysis, and we demonstrate that BRBC resists against a set of known attacks in the blockchain network. Finally, we simulate a blockchain network to assert the mechanism scalability and resilience to malicious actions in various network scenarios and different rates of malicious actions. The results show BRBC to be efficient to expel all nodes that acted with more than 50% of malicious actions.