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Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations

Author

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  • Denis Bouyssou

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Marc Pirlot

    (Faculté polytechnique de Mons - UMONS - Université de Mons / University of Mons)

Abstract

This paper analyzes conjoint measurement models allowing for intransitive and/or incomplete preferences. This analysis is based on the study of marginal traces induced on coordinates by the preference relation and uses conditions guaranteeing that these marginal traces are complete. Within the framework of these models, we propose a simple axiomatic characterization of preference relations compatible with the notion of dominance. We show that all such relations have a nontrivial numerical representation. Our results allow us to establish useful connections between two lines of thought in the area of decision analysis with multiple attributes that have largely remained unrelated: the one based on conjoint measurement and the one emphasizing the idea of dominance.

Suggested Citation

  • Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    • Handle: RePEc:hal:journl:hal-00004104
    DOI: 10.1016/j.jmp.2004.02.005
    Note: View the original document on HAL open archive server: https://hal.science/hal-00004104
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    References listed on IDEAS

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    Cited by:

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    2. Pelegrina, Guilherme Dean & Duarte, Leonardo Tomazeli & Grabisch, Michel & Romano, João Marcos Travassos, 2020. "The multilinear model in multicriteria decision making: The case of 2-additive capacities and contributions to parameter identification," European Journal of Operational Research, Elsevier, vol. 282(3), pages 945-956.
    3. Andrea C. Hupman & Jay Simon, 2023. "The Legacy of Peter Fishburn: Foundational Work and Lasting Impact," Decision Analysis, INFORMS, vol. 20(1), pages 1-15, March.
    4. Michel Grabisch & Salvatore Greco & Marc Pirlot, 2008. "Bipolar and bivariate models in multi-criteria decision analysis: descriptive and constructive approaches," Post-Print halshs-00340374, HAL.
    5. Patrick Meyer & Grégory Ponthière, 2011. "Eliciting Preferences on Multiattribute Societies with a Choquet Integral," Computational Economics, Springer;Society for Computational Economics, vol. 37(2), pages 133-168, February.
    6. Grabisch, Michel, 2006. "Representation of preferences over a finite scale by a mean operator," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 131-151, September.
    7. Mikhail Timonin, 2015. "Axiomatization of the Choquet integral for 2-dimensional heterogeneous product sets," Papers 1507.04167, arXiv.org, revised Mar 2016.
    8. Rubina Canesi & Chiara D’Alpaos, 2024. "The Evaluation of Sustainable Development Projects in Marginal Areas: An A’WOT Approach," Land, MDPI, vol. 13(5), pages 1-15, April.

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