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Aggregation of Semi-Orders: Intransitive Indifference Makes a Difference

Author

Listed:
  • 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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    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. Nobuo Koida, 2021. "Intransitive indifference with direction-dependent sensitivity," KIER Working Papers 1061, Kyoto University, Institute of Economic Research.
    3. Vila, Xavier, 1998. "On the Intransitivity of Preferences Consistent with Similarity Relations," Journal of Economic Theory, Elsevier, vol. 79(2), pages 281-287, April.
    4. Gustav Alexandrie, 2023. "Two impossibility results for social choice under individual indifference intransitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(4), pages 919-936, November.
    5. 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.
    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.
    7. 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.
    8. Daniele Caliari & Henrik Petri, 2025. "The Luce Model, Regularity, and Choice Overload," Papers 2502.21063, arXiv.org.

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