The Quality of Ranking during Simulated Pairwise Judgments for Examined Approximation Procedures

Abstract

An overview of current debates and contemporary research devoted to the modeling of decision-making processes and their facilitation directs attention to the quality of priority ratios estimation through pairwise comparisons. At the core of the process are various approximation procedures for a pairwise comparison matrix which, in a sense, reflects preferences of decision-makers. Certainly, when judgments regarding these preferences are perfectly consistent (cardinally transitive), all approximation procedures coincide and the quality of the prioritization process is exemplary. However, human judgments are very rarely consistent, and thus the quality of priority ratios estimation may significantly vary. Obviously, the range of these variations depends on the applied approximation procedure for a pairwise comparison matrix. Although there are many approximation procedures which can be applied in the prioritization process, it has been promoted for many decades that only one should be applied and no others qualify. This paper suggests this opinion is a fallacy. Research results argue that a genuine, commonly applied approximation procedure for a pairwise comparison matrix may deteriorate the quality of priority ratios estimation. Thus, a number of solutions are also proposed which can improve the process of priority ratios estimation. In order to provide credible and high quality results, the problem is studied via a properly designed and coded seminal simulation algorithm, executed in Wolfram Mathematica 8.0.