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Psychology
Cognitive Science

Ear Decomposition for Pair Comparison Data

Profile image of Martin LagesMartin Lages

2002, Journal of Mathematical Psychology

Abstract

An efficient graph-theoretical decomposition technique is introduced that treats inconsistencies in behavioral data as systematic adaptations rather than random errors. This technique, which is known as ear decomposition, reduces inconsistencies in any binary data set to a basis of directed cycles. Such a basis characterizes the data set in terms of inconsistencies and its size offers an improved measure of internal consistency. In two examples it is illustrated how different implementations of the ear decomposition technique can help to identify choices that are critical for violations of transitivity.

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This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons. However, it wrongly assumes that an inconsistency indicator can take values in any abelian linearly ordered group. The followup publication (On normalization of inconsistency indicators in pairwise comparisons, a collaboration which includes two of three authors of this publication) shows that any inconsistency indicator should be normalized for a number of practical and theoretical reasons. The publication below fails to demonstrate even one example of a non trivial group (other than a group consisting of real numbers. However, some obtained results (under erroneous assumptions) are still valid.

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Related topics

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