On the mean random inconsistency index of analytic hierarchy process

In this paper, the authors find a closed-form expression for the largest eigenvalue of a three-dimensional random pairwise comparison matrix. This expression can give all the corresponding distribution moments. In particular, the exact value of the mean and variance of the largest eigenvalue associated with a three-dimensional random pairwise comparison matrix are calculated, and are compared with those obtained by others on the topic. For n=4,...,15, the mean and variance are determined by simulation. The number of simulation runs are determined by taking both the absolute and the relative simulation errors into consideration.