Rank Reversal as a Source of Uncertainty and Manipulation in the PROMETHEE II Ranking: A First Investigation (original) (raw)

Abstract

PROMETHEE II is an aggregating procedure based on pairwise comparisons for ranking alternatives evaluated on multiple criteria. As other outranking methods, PROMETHEE II does not satisfy the assumption of independence to third alternatives. In other words, the ranks of two given alternatives may be influenced by the presence of a third one. This phenomenon, also called rank reversal, can be viewed as a source of uncertainty on the final ranking. Additionally, it raises the natural question of possible rank manipulations by adding ”well-chosen” alternatives. This problem is studied in the context of a simplified version of the PROMETHEE II method also known as the Copland score. A linear program is proposed to test whether there is a way to rank a given alternative at the first position by adding artificial ones. Simulations are used to quantify the likelihood of this possibility and to test if it can be avoided.

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Authors and Affiliations

  1. Computer & Decision Engineering (CoDE) Department, Ecole Polytechnique de Bruxelles, Université Libre de Bruxelles, Brussels, Belgium
    Julien Roland, Yves De Smet & Céline Verly

Authors

  1. Julien Roland
  2. Yves De Smet
  3. Céline Verly

Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy
    Salvatore Greco & Benedetto Matarazzo &
  2. CNRS UMR 7606, DAPA, LIP6 8, Université Pierre et Marie Curie - Paris6, rue du Capitaine Scott, F-75015, Paris, France
    Bernadette Bouchon-Meunier
  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy
    Giulianella Coletti
  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy
    Mario Fedrizzi
  5. Machine Intelligence Institute — IONA College,, 10801, New Rochelle, NY, USA
    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Roland, J., De Smet, Y., Verly, C. (2012). Rank Reversal as a Source of Uncertainty and Manipulation in the PROMETHEE II Ranking: A First Investigation. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8\_35

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