Detecting and Debugging Erroneous Statements in Pairwise Comparison Matrices

Reinhold Decker, Martin Meißner and Sören W. Scholz
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Reinhold Decker: Bielefeld University
Martin Meißner: Bielefeld University
Sören W. Scholz: Bielefeld University

A chapter in Operations Research Proceedings 2007, 2008, pp 277-282 from Springer

Abstract: Abstract Paired comparisons are a widely used technique for evaluating decision elements. If measured on a ratio scale, the judgments form a pairwise comparison matrix that can be interpreted as a ratio preference network. The collection of paired comparisons is often accompanied by manifold response errors driven by variations in attention, mood, mental efficiency, or the general mental state of the respondents. Such erroneous statements might seriously impair the consistency of the responses, and thus, the relative weights derived from the ratio preference network. This paper presents a new error detection approach that identifies deficient elements in pairwise comparison matrices and significantly reduces the mentioned effects with regard to the weights of the considered decision elements. It is based on the geometric mean of all connecting paths of the respective pairwise comparison matrix. Its basic applicability is demonstrated by means of Monte Carlo simulations.

Keywords: Mean Square Error; Paired Comparison; Preference Structure; Pairwise Comparison Matrix; Pairwise Comparison Matrice (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:oprchp:978-3-540-77903-2_43

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DOI: 10.1007/978-3-540-77903-2_43

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