Pairwise comparison matrices and the error-free property of the decision maker

Abstract

Pairwise comparison is a popular assessment method either for deriving criteria-weights or for evaluating alternatives according to a given criterion. In real-world applications consistency of the comparisons rarely happens: intransitivity can occur. The aim of the paper is to discuss the relationship between the consistency of the decision maker—described with the error-free property—and the consistency of the pairwise comparison matrix (PCM). The concept of error-free matrix is used to demonstrate that consistency of the PCM is not a sufficient condition of the error-free property of the decision maker. Informed and uninformed decision makers are defined. In the first stage of an assessment method a consistent or near-consistent matrix should be achieved: detecting, measuring and improving consistency are part of any procedure with both types of decision makers. In the second stage additional information are needed to reveal the decision maker’s real preferences. Interactive questioning procedures are recommended to reach that goal.

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Correspondence to József Temesi.

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The research was partly supported by the Hungarian National Research Fund, Grant K 77420.

The first version of this paper was presented at the 19th International Conference on Multiple Criteria Decision Making in Auckland, New Zealand, January 2008. This revised paper used valuable comments from an anonymous reviewer.

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Temesi, J. Pairwise comparison matrices and the error-free property of the decision maker. Cent Eur J Oper Res 19, 239–249 (2011). https://doi.org/10.1007/s10100-010-0145-8

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Keywords

  • Decision making
  • Pairwise comparisons
  • Consistency
  • Error-free matrices