Analysis of the sum of the inverse column sums (SICS): an alternative consistency measure for pairwise comparisons

Pairwise comparison matrices are fundamental to the analytic hierarchy process (AHP). Resolving the constructed pairwise comparison matrices produces both relative weights and a measure of consistency. The purpose of this paper is to discuss another alternative as a measure for consistency. As a solution to the drawbacks of existing consistency measures, a method called the sum of the inverse column sums (SICS) for pairwise comparison matrices was introduced. The SICS metric has the advantages of being easy to calculate, therefore it can be readily adapted to spreadsheet applications. This paper develops a theoretical basis establishing the validity for using the SICS method and a proof of the key boundedness conjecture. The primary means of generating results is not a mathematical approach, but a simulation approach coupled with statistical arguments