A Monte Carlo Study of Parwise Comparison

The pairwise comparison methodology introduced by Thurston in 1927 (see [12]) can be used as a powerful inference tool and knowledge acquisition technique in knowledge-based systems. The goal of pairwise comparisons is to establish the relative preferences of n stimuli in situations in which it is impractical (or meaningless) to provide estimates for the stimuli. To this end, an expert provides pairwise comparison coefficients a ij >0 which are meant to be a substitute for the quotients s i /s j of the unknown (or undefined) values s i ,s j >0. There has been an ongoing discussion about which method fdor finding solutions to a pairwise comparison matrix is better [11,2]. It is not clear whether or not an analytical proof can be devised. This seems to be a good reason for formulating the problem as an empirical experiment using a Monte Carlo approach.