Fischer, Lynch and Paterson showed in a fundamental paper that achieving a distributed agreement for N > I processors is impossible in the presence of one faulty processor. This result was later extended by Moran and Wolfstahl who showed that it holds for any task with a connected input graph and a disconnected decision graph (whcrc a vcrtcx in the input [decision] graph is an N-tuple of input [decision] values of the processors, and there is an edge connecting two vertices if and only if they differ in exactly one component),
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Biran et al. (1988) studied this question.