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Aggregation of Semi-Orders: Intransitive Indifference Makes a Difference

Author

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  • Itzhak Gilboa

    (Northwestern University [Evanston])

  • Robert Lapson

    (Northwestern University [Evanston])

Abstract

A semiorder can be thought of as a binary relation P for which there is a utilityu representing it in the following sense: xPy iffu(x) −u(y) > 1. We argue that weak orders (for which indifference is transitive) can not be considered a successful approximation of semiorders; for instance, a utility function representing a semiorder in the manner mentioned above is almost unique, i.e. cardinal and not only ordinal. In this paper we deal with semiorders on a product space and their relation to given semiorders on the original spaces. Following the intuition of Rubinstein we find surprising results: with the appropriate framework, it turns out that a Savage-type expected utility requires significantly weaker axioms than it does in the context of weak orders.

Suggested Citation

  • Itzhak Gilboa & Robert Lapson, 1995. "Aggregation of Semi-Orders: Intransitive Indifference Makes a Difference," Post-Print hal-00753141, HAL.
    • Handle: RePEc:hal:journl:hal-00753141
    DOI: 10.1007/BF01213647
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    References listed on IDEAS

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    1. Avraham Beja & Itzhak Gilboa, 1989. "Numerical Representations of Imperfectly Ordered Preferences (A Unified Geometric Exposition," Discussion Papers 836, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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    Cited by:

    1. Nuh Aygün Dalkıran & Furkan Yıldız, 2021. "Another Characterization of Expected Scott-Suppes Utility Representation," Bogazici Journal, Review of Social, Economic and Administrative Studies, Bogazici University, Department of Economics, vol. 35(2), pages 177-193.
    2. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    3. Nobuo Koida, 2021. "Intransitive indifference with direction-dependent sensitivity," KIER Working Papers 1061, Kyoto University, Institute of Economic Research.
    4. Manzini Paola & Mariotti Marco, 2006. "A Vague Theory of Choice over Time," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-29, October.
    5. Vila, Xavier, 1998. "On the Intransitivity of Preferences Consistent with Similarity Relations," Journal of Economic Theory, Elsevier, vol. 79(2), pages 281-287, April.
    6. 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.

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