Analysis of Rank Reversal in Analytic Hierarchy Process

This technical report examines the claims made by Belton and Gear regarding their revised method intended to prevent the rank reversal phenomenon in the analytic hierarchy process. The authors argue that the method proposed by Belton and Gear is flawed and fails to maintain the necessary ratios among alternatives, ultimately leading to the persistence of rank reversal. The report presents a counter-example using two different approaches to illustrate the shortcomings of the revised method. It emphasizes the need for researchers to revert to Saaty's original theories, suggesting that rank reversal should be viewed as a practical issue in decision-making rather than a theoretical one. The authors advocate for adherence to Saaty's four methods based on criteria characteristics to effectively address the rank reversal phenomenon. The document includes references to prior research and discussions surrounding the topic, providing a comprehensive analysis of the implications of the revised method on decision-making processes.