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Independent preferences

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  • Vind, Karl

Abstract

A simple mathematical result characterizing a subset of a product set is proved and used to obtain additive representations of preferences. The additivity consequences of independence assumptions are obtained for preferences which are not total or transitive. This means that most of the economic theory based on additive preferences - expected utility, discounted utility - has been generalized to preferences which are not total or transitive. Other economic applications of the theorem are given.
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Suggested Citation

  • Vind, Karl, 1991. "Independent preferences," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 119-135.
    • Handle: RePEc:eee:mateco:v:20:y:1991:i:1:p:119-135
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    Cited by:

    1. Dino Borie, 2016. "Additively Separable Preferences Without the Completeness Axiom: An Algebraic Approach," GREDEG Working Papers 2016-11, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    2. Tangian, Andranik, 2004. "A model for ordinally constructing additive objective functions," European Journal of Operational Research, Elsevier, vol. 159(2), pages 476-512, December.
    3. Craig Webb, 2013. "Bargaining with subjective mixtures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 15-39, January.
    4. Aurélien Baillon & Olivier L’Haridon, 2021. "Discrete Arrow–Pratt indexes for risk and uncertainty," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(4), pages 1375-1393, November.
    5. 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.
    6. Yutaka Nakamura, 1997. "Lexicographic Additivity For Multi-Attribute Preferences On Finite Sets," Theory and Decision, Springer, vol. 42(1), pages 1-19, January.
    7. Ebbe Groes & Hans Jacobsen & Birgitte Sloth & Torben Tranæs, 1999. "Testing the Intransitivity Explanation of the Allais Paradox," Theory and Decision, Springer, vol. 47(3), pages 229-245, December.
    8. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2022. "A note on ELECTRE TRI-nB with few limiting profiles," 4OR, Springer, vol. 20(3), pages 443-463, September.
    9. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    10. Vind, Karl, 2000. "von Neumann Morgenstern preferences," Journal of Mathematical Economics, Elsevier, vol. 33(1), pages 109-122, February.
    11. O'Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," Economic Research Papers 270751, University of Warwick - Department of Economics.
    12. Bouyssou, Denis & Marchant, Thierry, 2010. "Additive conjoint measurement with ordered categories," European Journal of Operational Research, Elsevier, vol. 203(1), pages 195-204, May.
    13. Nakamura, Yutaka, 1998. "Skew-symmetric additive representations of preferences," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 367-387, October.
    14. Grant, Simon & Kajii, Atsushi & Polak, Ben, 2000. "Decomposable Choice under Uncertainty," Journal of Economic Theory, Elsevier, vol. 92(2), pages 169-197, June.
    15. Karni, Edi & Schmeidler, David, 1990. "Utility Theory and Uncertainty," Foerder Institute for Economic Research Working Papers 275480, Tel-Aviv University > Foerder Institute for Economic Research.
    16. Denis Bouyssou & Thierry Marchant, 2011. "Subjective expected utility without preferences," Working Papers hal-00606939, HAL.
    17. Ok, Efe A. & Masatlioglu, Yusufcan, 2007. "A theory of (relative) discounting," Journal of Economic Theory, Elsevier, vol. 137(1), pages 214-245, November.
    18. Qin, Wei-Zhi & Rommeswinkel, Hendrik, 2022. "Additive representations on a simplex," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    19. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    20. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    21. Bouyssou, Denis & Pirlot, Marc, 2005. "Following the traces:: An introduction to conjoint measurement without transitivity and additivity," European Journal of Operational Research, Elsevier, vol. 163(2), pages 287-337, June.
    22. Peter C. Fishbur, 1992. "A general axiomatization of additive measurement with applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(6), pages 741-755, October.
    23. Denis Bouyssou & Thierry Marchant & Marc Pirlot, 2021. "A note on ELECTRE TRI-nB with few limiting profiles," Post-Print hal-02917998, HAL.
    24. O’Callaghan, Patrick, 2011. "Context and Decision: Utility on a Union of Mixture Spaces," The Warwick Economics Research Paper Series (TWERPS) 973, University of Warwick, Department of Economics.
    25. Qin, Wei-zhi & Rommeswinkel, Hendrik, 2017. "Conditionally Additive Utility Representations," MPRA Paper 78158, University Library of Munich, Germany.

    More about this item

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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