Comparison of group inconsistency and the arithmetic mean of individual inconsistencies

This paper investigates the inconsistency rate in group decision-making within the framework of the Group Analytic Hierarchy Process (GAHP), a method that aggregates individual judgments to form a group pairwise comparison matrix. The primary objective is to prove that the group's inconsistency rate does not exceed the arithmetic mean of the individual inconsistency rates. Utilizing Jensen's inequality as the mathematical foundation, we demonstrate that integrating individual judgments effectively reduces the overall group inconsistency rate, aligning it closely with the average inconsistency of individual members. The findings decidedly confirm that, underpinned by Jensen's inequality, the group inconsistency rate will never surpass the mean individual inconsistency rate. This result substantially enhances the theoretical understanding and practical reliability of GAHP, contributing to more accurate and effective group decision-making processes.

کلیدواژه ها:

Group inconsistency rate ، Arithmetic mean of individual inconsistency ، Jensen's inequality ، Judgment aggregation ، Group analytic hierarchy process (GAHP) ، Multiple-criteria decision-making (MCDM)