Theoretical analysis proves identical ordering between two consistency indices in 3rd-order pairwise comparison matrices, confirming experimental observations.
In AHP, a number of consistency indices have been proposed.Saaty's C.I. is a pioneer and generally adopted by users of AHP.We also proposed a new consistency index with the aid of the characteristic polynomial of the pairwise comparison matrix.Surprisingly, 3rd order random matrices make the completely same numerical order of two consistency indices, i.e.Saaty's C.I. and our consistency index.In this short paper, we show this experimental result is theoretically correct.
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Shiraishi et al. (2021) studied this question.
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