# Towards quantification of incompleteness in the pairwise comparisons method

## TL;DR

This paper introduces four simple indices to quantify the impact of missing data in pairwise comparison matrices, linking incompleteness with inconsistency and sensitivity in decision-making.

## Contribution

It develops and validates new indices for measuring incompleteness in pairwise comparisons, aiding quick assessment of data quality impact.

## Key findings

- Incompleteness and inconsistency equally affect matrix sensitivity.
- Proposed indices effectively estimate the impact of missing data.
- Monte Carlo experiments confirm the indices' usefulness.

## Abstract

Alongside consistency, completeness of information is one of the key factors influencing data quality. The objective of this paper is to define ways of treating missing entries in pairwise comparisons (PC) method with respect to inconsistency and sensitivity. Two important factors related to the incompleteness of PC matrices have been identified, namely the number of missing pairwise comparisons and their arrangements. Accordingly, four incompleteness indices have been developed, simple to calculate, each of them take into account both: the total number of missing data and their distribution in the PC matrix. A numerical study of the properties of these indices has been also conducted using a series of Montecarlo experiments. It demonstrated that both incompleteness and inconsistency of data equally contribute to the sensitivity of the PC matrix. Although incompleteness is only just one of the factors influencing sensitivity, a relative simplicity of the proposed indices may help decision makers to quickly estimate the impact of missing comparisons on the quality of final result.