The usual approach to plausible reasoning is to associate a validity measure with each fact or rule, and to compute from these a validity measure for any deduction that is made. This approach is shown to be inappropriate for some classes of problems, particularly those in which the evidence is not internally consistent. Three current plausible reasoning architectures are summarised and each applied to the same small task. An analysis of the performance of these systems reveals deficiencies in each case. The paper then outlines a new approach based on the discovery of consistent subsets of the given evidence. This system can be used either in isolation or in conjunction with a validity-propagating architecture. Comparative results from implementations of all four systems are presented.