The replies by Saaty (1990) and by Harker and Vargas (1990) to my remarks on the Analytic Hierarchy Process (Dyer 1990) are useful in focusing attention on areas of disagreement regarding the AHP, and provide readers with sufficient information to form their own opinions. The purpose of this response is not to extend the debate, but to clarify the two methods proposed in my paper to resolve the problem of rank reversal in the AHP. Harker and Vargas (1989) misinterpreted my first proposed method (Method 1) in their reply. The key observation they missed is that both the weights on the criteria and the scores of the alternatives on the criteria must be normalized with respect to the same range of alternative values. In Method 1, the decision maker must specify the ranges over which he assumed the alternatives might vary on each criterion when he determined the weights. An example may be useful in clarifying the key ideas. Suppose each alternative in the Harker and Vargas (1990) example represents the choice of a decision maker among sums of money deposited in two different bank accounts, and each criterion is simply the amount of money deposited in a single bank account. Obviously, the decision maker would use the sum of the accounts as the basis for ranking the alternatives, and would select B from the three alternatives A, B, and C. Let us see how the appropriate use of Method 1 would lead to this result without recourse to the supermatrix technique or to the concept of dependence of the criteria on the alternatives. The decision maker would consider the deposits in each bank account to be equally important if he assumed that the ranges of the possible deposits were equal. For example, suppose the decision maker assumes that the values for each bank account (criterion) vary over the range [1, 80] . He responds that changes from 1 to 80 on each criterion are equally important, so the normalized eigenvector for the AHP criterion weights is (1/2, 1/2). Using Method 1, since the range of values on criterion C1 is [75, 80], and the decision maker assumed a range of [1, 80] in determining the equal criterion weights, we must introduce a "dummy" alternative with the value of 1 on criterion C1 (this "dummy" alternative does not need to be explicitly introduced with values on the other criteria, but it could be and would not affect the results as long as its assumed values on the other criteria are in the range [1, 80]). Similarly, a "dummy" alternative with a value of 80 must be introduced for criterion C2. The normalized eigenvector for criterion C1 would become (80/235, 79/235, 75 /235, 1/235), for example, where the last component 1/235 is the score for the "dummy" alternative. We normalize each resulting eigenvector by subtracting its smallest component, and then dividing by the largest component. The appropriate scores for the three alternatives are