An essay on rank preservation and reversal

Saaty T. L., Sağır M.

MATHEMATICAL AND COMPUTER MODELLING, vol.49, pp.1230-1243, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 49
  • Publication Date: 2009
  • Doi Number: 10.1016/j.mcm.2008.08.001
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1230-1243
  • Keywords: Analytic hierarchy process, Adding alternatives, Decision making, Phantom alternatives, Priorities, Rank reversal
  • Eskisehir Osmangazi University Affiliated: Yes


Rank preservation and reversal, so fundamental in decision making, have been an unresolved issue in the field of economics and utility theory and came into focus when the Analytic Hierarchy Process was developed because it uses paired comparisons that inevitably make the priorities of the alternatives interdependent. This paper summarizes the important issues that can play a role in rank preservation and reversal with counterexamples to show that preserving rank in all situations is wrong. (C) 2008 Elsevier Ltd. All rights reserved.