Abstract The object of this paper is to demonstrate how critics can mislead themselves and others in pursuing examples and ideas that draw false conclusions. The Analytic Hierarchy Process (AHP) has clear requirements that involve both the hierarchical structure and the priorities in the structure. Any example that purports to show that the AHP does not give correct results must first follow these requirements. Here we take some of these examples and show that by correctly structuring and setting the priorities they do give the expected results. The most common misconception is that the AHP should be able to reproduce results in a specific situation from a scientific formula without including enough data from the outside world to represent the situation in an AHP model. Scientific formulas (usually involving combinations of mathematical operations: adding, multiplying, raising factors to powers) have been arrived at through the ages based on experience, the need to make results fit some kind of measuring device, and pure whim. To make an AHP model reproduce the results of these myriads of formulas one must understand the precepts of AHP very well so that the AHP model can be set up properly to incorporate the data. We examine a few of these examples and show how they should be properly modeled for AHP to give the expected results.