Pairwise Comparisons Rating Scale Paradox

TL;DR

This paper identifies a paradox in pairwise comparisons rating scale data caused by incorrect data entry, and proposes a normalization-based correction to improve the accuracy of weight calculations.

Contribution

It introduces a normalization method to correct data entry errors in pairwise comparisons rating scales, addressing a widespread paradox in the field.

Findings

Unprocessed rating scale data cause a paradox in weight calculation.

Normalization effectively corrects data entry errors.

Improves accuracy of pairwise comparison methods.

Abstract

This study demonstrates that incorrect data are entered into a pairwise comparisons matrix for processing into weights for the data collected by a rating scale. Unprocessed rating scale data lead to a paradox. A solution to it, based on normalization, is proposed. This is an essential correction for virtually all pairwise comparisons methods using rating scales. The illustration of the relative error currently, taking place, is discussed.