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Delegated Byzantine Fault Tolerance (dBFT) is a sophisticated algorithm meant to facilitate consensus on a blockchain. Although it is not in common use as of yet, it represents an alternative to simpler proof of stake, proof of importance and proof of work methods.
The story of this as-of-yet theoretical algorithm is fascinating – it is meant to address a particular old-school game theory problem called the Byzantine generals' problem. In this scenario, there are a number of generals formulating a plan to attack a city. Consensus needs to be met, since anything less than a consensus leads to significant battle failures. However, there are communication difficulties, and there is an additional concern – in the Byzantine generals' problem, planners have to look out for individual treacherous actors – actors who may not even report the same decision to all involved parties.
In the blockchain world, this is explained by pointing out that while some node operators are professionals, others are amateurs with a less sophisticated view of markets and game theory and everything else. They cannot be counted on, so this is the complex issue that Delegated Byzantine Fault Tolerance addresses. In order to handle this uncertainty, Delegated Byzantine Fault Tolerance uses a two-thirds rule and other elements to make sure that consensus is achieved even with a lot of unknowns.