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Additively Separable Preferences Without the Completeness Axiom: An Algebraic Approach

Author

Listed:
  • Dino Borie

    (GREDEG CNRS
    University of Nice Sophia Antipolis)

Abstract

A simple mathematical result characterizing a partially ordered mean groupoid is proved and used to study the problem of additively separable preferences on preordered Cartesian product set. This means that most of the economic theory based on separable preferences - expected utility,rank-dependent expected utility, qualitative probability, discounted utility - could be generalized to the multi-utility approach.

Suggested Citation

  • 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.
    • Handle: RePEc:gre:wpaper:2016-11
    as

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    File URL: http://195.220.190.85/GREDEG-WP-2016-11.pdf
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    References listed on IDEAS

    as
    1. Vind, Karl, 1991. "Independent preferences," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 119-135.
    2. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    3. Mohammed Abdellaoui, 2002. "A Genuine Rank-Dependent Generalization of the Von Neumann-Morgenstern Expected Utility Theorem," Econometrica, Econometric Society, vol. 70(2), pages 717-736, March.
    4. Chateauneuf, Alain & Wakker, Peter, 1999. "An Axiomatization of Cumulative Prospect Theory for Decision under Risk," Journal of Risk and Uncertainty, Springer, vol. 18(2), pages 137-145, August.
    5. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
    6. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    7. Baucells, Manel & Shapley, Lloyd S., 2008. "Multiperson utility," Games and Economic Behavior, Elsevier, vol. 62(2), pages 329-347, March.
    8. Gerard Debreu, 1959. "Topological Methods in Cardinal Utility Theory," Cowles Foundation Discussion Papers 76, Cowles Foundation for Research in Economics, Yale University.
    9. Galaabaatar, Tsogbadral & Karni, Edi, 2012. "Expected multi-utility representations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 242-246.
    10. Karl Vind & Birgit Grodal, 1990. "Additive Utility Functions and Other Special Functions in Economic Theory," Discussion Papers 90-21, University of Copenhagen. Department of Economics.
    11. Eric Maskin, 1978. "A Theorem on Utilitarianism," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 45(1), pages 93-96.
    12. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 4(2), pages 155-161.
    13. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
    14. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    15. Wakker, Peter, 1993. "Additive representations on rank-ordered sets : II. The topological approach," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 1-26.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Additive utility; Separable utility; Completeness axiom; Incomplete preferences;
    All these keywords.

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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