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Reference-based preferences aggregation procedures in multi-criteria decision making

  • Rolland, Antoine
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    This paper aims at introducing and investigating a new family of merely qualitative models for multicriteria decision making. Such models do not require any numerical representation. Within this family, we will focus on decision rules using reference levels in order to help comparing several alternatives. We will investigate both the descriptive potential of such rules and their axiomatic foundations. After recalling the descriptive and prescriptive limitations of merely ordinal rules that do not use reference points, we will introduce a new axiom requiring that the Decision Maker’s preference between two alternatives depends on the respective positions of their consequences relatively to reference levels. Under this assumption we will determine the only possible form for the decision rule and characterize some particular instances of this rule under transitivity constraints. Our results show that introducing reference points overcomes the usual limitations of purely ordinal aggregation methods, by moving the application point of Arrow’s theorem.

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    File URL: http://www.sciencedirect.com/science/article/pii/S037722171200759X
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    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 225 (2013)
    Issue (Month): 3 ()
    Pages: 479-486

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    Handle: RePEc:eee:ejores:v:225:y:2013:i:3:p:479-486
    Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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    1. Fishburn, Peter C, 1975. "Axioms for Lexicographic Preferences," Review of Economic Studies, Wiley Blackwell, vol. 42(3), pages 415-19, July.
    2. Almeida-Dias, J. & Figueira, J.R. & Roy, B., 2010. "Electre Tri-C: A multiple criteria sorting method based on characteristic reference actions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 565-580, August.
    3. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2002. "Rough sets methodology for sorting problems in presence of multiple attributes and criteria," European Journal of Operational Research, Elsevier, vol. 138(2), pages 247-259, April.
    4. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    5. Jacquet-Lagreze, E. & Siskos, J., 1982. "Assessing a set of additive utility functions for multicriteria decision-making, the UTA method," European Journal of Operational Research, Elsevier, vol. 10(2), pages 151-164, June.
    6. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2001. "Rough sets theory for multicriteria decision analysis," European Journal of Operational Research, Elsevier, vol. 129(1), pages 1-47, February.
    7. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    8. Bouyssou, Denis & Pirlot, Marc, 2007. "Further results on concordance relations," European Journal of Operational Research, Elsevier, vol. 181(1), pages 505-514, August.
    9. Doumpos, M. & Marinakis, Y. & Marinaki, M. & Zopounidis, C., 2009. "An evolutionary approach to construction of outranking models for multicriteria classification: The case of the ELECTRE TRI method," European Journal of Operational Research, Elsevier, vol. 199(2), pages 496-505, December.
    10. repec:cup:cbooks:9780521003117 is not listed on IDEAS
    11. repec:cup:cbooks:9780521802345 is not listed on IDEAS
    12. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    13. Bouyssou, Denis & Pirlot, Marc, 2005. "A characterization of concordance relations," European Journal of Operational Research, Elsevier, vol. 167(2), pages 427-443, December.
    14. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
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