The consistency index in reciprocal matrices: Comparison of deterministic and statistical approaches |
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Authors: | Luis G Vargas |
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Institution: | The Joseph M. Katz Graduate School of Business, University of Pittsburgh, Pittsburgh, PA 15260, United States |
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Abstract: | When checking the inconsistency level of a positive reciprocal matrix Saaty uses a deterministic criterion based on two parameters, a benchmark (the average), and a consistency level, usually 10%. Using results from a simulation experiment with 100,000 positive random reciprocal matrices of size varying from 3 to 15, we developed a probabilistic criterion and compare it to Saaty’s index. We found that if a positive reciprocal matrix is consistent according to the deterministic criterion is also consistent according to the probabilistic criterion only if we accept a higher than usual probability of Type I error. Reducing this error implies that the benchmark must be a small percentile of the probability distribution of the consistency index. |
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Keywords: | Consistency Consistency ratio Random judgments Statistical consistency |
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