Inducement of nonexistent order by the analytic hierarchy process

An apparently unreported problem facing decision makers who use AHP is described. It is demonstrated that conventional AHP and some of its variants (the ideal mode, and the pairwise aggregated approach, PAHAP) can induce ordering even when no order exists. It is also shown that all three approaches can induce different orderings and that the orderings are sensitive to innocuous changes. Thus, even absent addition or deletion of alternatives, the decision maker relying on AHP or these variants can be seriously misled.