Remarks about inconsistency analysis in the pairwise comparison technique

Abstract

The prioritization of available alternatives is at the core of the multi-criteria decision making. It is typically done by assigning a priority weight to each of the alternatives. The weights indicate the alternatives' relative importance with respect to a given criterion. Many of prioritization methods are based on pairwise comparisons of the decision alternatives. As a result of such comparisons, a pairwise comparison matrix (PCM) that contains priority-weights-ratios is received. In this type of decision-making analysis a special attention is paid to so-called inconsistency analysis. It is a popular claim, that big errors in judgments about the priority ratios make the data contained in PCM useless. To “measure” the degree of PCM inconsistency various indices are proposed in literature. But the usage of these indices is justified only by some heuristics. In this paper we use simulation-based approach to the analysis of the relationships between the inconsistency indices and the errors of priority-vector's estimates. These relationships are examined under different simulation frameworks that reflect different requirements forced by the PCM-creation methodology. The simulation studies enable us to gain a deeper insight into the nature of pairwise comparisons methodology as well as new knowledge about the impact of various conventional assumptions, taken within the pairwise comparison approach, on the quality of the final priority-weights-estimates.