Inconsistency evaluation in pairwise comparison using norm-based distances

Michele Fedrizzi (), Nino Civolani and Andrew Critch
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Michele Fedrizzi: University of Trento
Nino Civolani: University of Trento
Andrew Critch: University of California, Berkeley

Decisions in Economics and Finance, 2020, vol. 43, issue 2, No 13, 657-672

Abstract: Abstract This paper studies the properties of an inconsistency index of a pairwise comparison matrix under the assumption that the index is defined as a norm-induced distance from the nearest consistent matrix. Under additive representation of preferences, it is proved that an inconsistency index defined in this way is a seminorm in the linear space of skew-symmetric matrices and several relevant properties hold. In particular, this linear space can be partitioned into equivalence classes, where each class is an affine subspace and all the matrices in the same class share a common value of the inconsistency index. The paper extends in a more general framework some results due, respectively, to Crawford and to Barzilai. It is also proved that norm-based inconsistency indices satisfy a set of six characterizing properties previously introduced, as well as an upper bound property for group preference aggregation.

Keywords: Inconsistency index; Pairwise comparison matrix; Norm; Distance (search for similar items in EconPapers)
JEL-codes: C44 D7 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10203-020-00304-9

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