# Eigenvector Method and rank reversal in group decision making revisited

## TL;DR

This paper revisits the Eigenvector Method in group decision making, demonstrating that rank reversal issues are linked to differences between right and inverse left eigenvector rankings, supported by a minimal counterexample.

## Contribution

It identifies the cause of rank reversal in the Eigenvector Method as the difference between right and inverse left eigenvector rankings and provides a minimal counterexample.

## Key findings

- Rank reversal occurs due to eigenvector ranking differences
- A minimal counterexample illustrates the problem
- Theoretical analysis clarifies the eigenvector ranking issue

## Abstract

It has been shown recently that the Eigenvector Method may lead to strong rank reversal in group decision making, that is, the alternative with the highest priority according to all individual vectors may lose its position when evaluations are derived from the aggregated group comparison matrix. We give a minimal counterexample and prove that this negative result is a consequence of the difference of the rankings induced by the right and inverse left eigenvectors.