An essay on rank preservation and reversal

Thomas Saaty
Joseph M. Katz Graduate School of Business
University of Pittsburgh
United States
Mujgan Sagir Ozdemir
Industrial Engineering
Eskisehir Osmangazi University

Publication date: Mar, 2009

Journal: Mathematical and Computer Modelling
Vol.: 49- Issue: 5-6- Pages: 1230-1243

Abstract: 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.

Keywords: Analytic Hierarchy Process, AHP, Adding alternatives, Decision making, Phantom alternatives, Priorities, Rank reversal