The Analytic Hierarchy Process (AHP) is a popular method for solving multi-criteria problems. Many researchers emphasize the simplicity and naturalness of the AHP procedure for evaluating alternatives. However, many scholars believe that the AHP is flawed and therefore cannot be applied in practice. Such a scattering of opinions requires an explanation. The method of AHP uses pairwise comparisons of alternatives. And it is based on the assumption that the alternatives can be measured on the scale of relations. Fechner’s psychophysical law is used as justification for the existence of method of measurement with ratio scales. But there are not one but two psychophysical laws. The existence of two psychophysical laws is a problem of psychophysics. This problem has been solved quite recently. It was shown that the basic psychophysical laws are equivalent. In order to solve this problem, an adjustment of Stevens’ direct measurement model was required. It is suggested that a direct measurement model be used to overcome the shortcomings of the Analytic Hierarchy Process. In this case, the fundamental AHP measurement scale can be used. The adjusted AHP method contains a direct measurement model and a built-in mechanism for checking the adequacy of measurement results. An example of direct measurement of alternatives is analyzed.