A Trend Analysis of Rank Reversal in Widely Used Decision‐Making Methods

Abstract

Rank reversal is a phenomenon that can occur with various proposed decision‐making methods when the rank order of alternatives changes by the inclusion or removal of an uninformative alternative. This survey provides a trend analysis of five widely used decision‐making methods that are subject to rank reversal: (i) the Analytic Hierarchy Process (AHP), (ii) the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), (iii) the Preference Ranking Organisation METHod for Enrichment Evaluations (PROMETHEE), (iv) the ÉLimination Et Choix Traduisant la REalité (ELECTRE), which means Elimination and Choice Translating Reality and (v) the VIse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR), which means: Multicriteria Optimization and Compromise Solution in Serbian. The trend analysis also segments the literature based on three categories: (i) literature that proposes a modified procedure of a decision‐making method to correct for rank reversal; (ii) literature that identifies the root cause of rank reversal within a method and (iii) literature that evaluates a proposed method based on its potential for rank reversal. The first observation of this paper is that despite the importance of choosing a method for decision‐making that avoids rank reversal, and despite several publications on the effects of this issue, applications using methods prone to rank reversal continue to be widely used. Further, by tracing historical publication trends across the three categories, this paper shows how rank reversal research has developed over time, with research on correcting rank reversal (Category 1) remaining steady and dominant, while root‐cause analysis of rank reversal within a method (Category 2) and evaluative work (Category 3) are growing. The survey ends by highlighting other methods that are prone to rank reversal but have not had sufficient literature drawing attention to their susceptibility to this issue. Examples include the Min–Max Regret method and the Characteristic Objects Method (COMET) of decision‐making. We hope that this work draws further attention and sensitivity to the implications of rank reversal in newly proposed and existing decision‐making applications and that it would enable a discussion that would be beneficial to various researchers and practitioners in the broader field of decision‐making.