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Consider a synchronous network of n players, each with a local input. The goal of distributed consensus is to globally agree on one of the valid inputs even if some non-trivial subset of the players are faulty. By valid input, we mean the input of any non-faulty player. Extant results in Byzantine agreement literature capture the behaviour of faulty players in an "all-or-nothing" fashion. For instance, a (Byzantine) faulty player is completely unconstrained and could behave differently with different players. This leads to a gross underestimation of the achievable fault-tolerance. In this work, we propose a fault-model that considerably improves the estimation of fault-tolerance and helps capture real-life scenarios better. For instance, if two (honest) players were part of the same LAN (which is essentially a broadcast network), it is impossible for a external faulty player to behave differently with these two players (though the faulty player may behave with "equal" malice with both these players!). Among our results, we introduce the sectional fault-model that is more general and can capture practical scenarios not captured by any extant model. We provide a complete characterization of the tolerable faults and present efficient protocols to achieve consensus. We remark that the results of this paper strictly generalize the extant characterizations of fault-tolerance. For example, consider a network of four players P1,P2,P3 and P4, under the corrupting influence of a Byzantine adversary given by the adversary structure A = {(P1, P2), (P2, P3), (P4)}. Agreement is impossible in such a scenario, since the three sets from .A cover the player set. However, it would be evident from our results that con-?Financial support from Infosys Technologies Limited, India, is acknowledged. :?This author would like to thank Prof, Kwangjo Kim, ICU, South Korea, for several helpful discussions. The financial support from the Ministry of Information Technology, Government of South Korea is also warmly acknowledged.

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