In this paper, we use Saaty's Eigenvector Method and the Power Method as well as Ω=1, 2, ⋯ , 9, 1/2, 1/3, ⋯ , 1/9} and Ω-={1,2, ⋯ ,9,1, 1/2, ⋯ ,1/9} as the sets from which the pairwise comparison judgments are assigned at random to examine the variation in the values determined for the mean random consistency index. By extensive simulation analysis, we found that both methods produce the same values for the mean (...) random consistency random index. Also, we found that the reason for producing two different sets of values is the use of Ω vs. Ω- and not the selection of the Power Method vs. Saaty's Eigenvector Method. (shrink)