Inconsistency indicator maps on groups for pairwise comparisons

TL;DR

This paper explores using abelian groups to analyze inconsistency in pairwise comparisons but incorrectly assumes these indicators can take values in any such group, leading to flawed but partially valid results.

Contribution

It introduces an abelian group framework for inconsistency analysis but incorrectly assumes unnormalized indicators can be in any abelian linearly ordered group.

Findings

Some results are valid despite incorrect assumptions

Highlights the need for normalization of inconsistency indicators

Demonstrates limitations of using arbitrary abelian groups

Abstract

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.