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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), University of Nice Sophia Antipolis.
  • Handle: RePEc:gre:wpaper:2016-11
    as

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    File URL: http://www.gredeg.cnrs.fr/working-papers/GREDEG-WP-2016-11.pdf
    File Function: First version, 2016
    Download Restriction: no

    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. Baucells, Manel & Shapley, Lloyd S., 2008. "Multiperson utility," Games and Economic Behavior, Elsevier, vol. 62(2), pages 329-347, March.
    7. Galaabaatar, Tsogbadral & Karni, Edi, 2012. "Expected multi-utility representations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 242-246.
    8. 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.
    9. Paul A. Samuelson, 1937. "A Note on Measurement of Utility," Review of Economic Studies, Oxford University Press, vol. 4(2), pages 155-161.
    10. 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.
    11. 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)

    More about this item

    Keywords

    Additive utility; Separable utility; Completeness axiom; Incomplete preferences;

    JEL classification:

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

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