Inverse inconsistency in Analytic Hierarchies

This paper discusses a fundamental problem in the Analytic Hierarchy Process of T.L. Saaty, namely inverse inconsistency, previously addressed only indirectly in the literature. A mechanism for handling this is suggested. More importantly, it is demonstrated how the problem is less significant in the Modified Analytic Hierarchy Process devised by Donegan et al. The related problem of dependence upon the irrelevant alternative is also examined and a list of statistically significant Random Indexes for the modified process is presented.