A Monte Carlo study of pairwise comparison

The pairwise comparison methodology introduced by Thurstone (1927) can be used as a powerful inference tool and knowledge acquisition technique in knowledge-based systems. The practical and theoretical virtue of the pairwise comparison methodology is its simplicity. The goal of pairwise comparisons is to establish the relative preferences of n stimuli in situations in which it is impractical to provide estimates for the stimuli. A n x n pairwise comparison matrix is defined simply as a square matrix in essence. Solutions obtained by 2 methods, geometric mean (GM) and eigenvector (EV), turned out to be close enough to the given input matrix. Both methods are accurate enough for most practical applications. It is improbable that an analytical solution can be devised in a situation where the results favor GM over EV for one metric while favoring EV over GM or another metric. More importantly, statistical evidence of convergence to a solution has been observed.