An overview of current debates and contemporary research devoted to the modeling of decision making processes and their facilitation directs attention to the Analytic Hierarchy Process (AHP). At the core of the AHP are various prioritization procedures (PPs) and consistency measures (CMs) for a Pairwise Comparison Matrix (PCM) which, in a sense, reflects preferences of decision makers. Certainly, when judgments about these preferences are perfectly consistent (cardinally transitive), all PPs coincide and the quality of the priority ratios (PRs) estimation is exemplary. However, human judgments are very rarely consistent, thus the quality of PRs estimation may significantly vary. The scale of these variations depends on the applied PP and utilized CM for a PCM. This is why it is important to find out which PPs and which CMs for a PCM lead directly to an improvement of the PRs estimation accuracy. The main goal of this research is realized through the properly designed, coded and executed seminal and sophisticated simulation algorithms in Wolfram Mathematica 8.0. These research results convince that the embedded in the AHP and commonly applied, both genuine PP and CM for PCM may significantly deteriorate the quality of PRs estimation; however, solutions proposed in this paper can significantly improve the methodology.