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A representation of interval orders through a bi-utility function

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  • Yann Rébillé

    (LEMNA - Laboratoire d'économie et de management de Nantes Atlantique - Nantes Univ - IAE Nantes - Nantes Université - Institut d'Administration des Entreprises - Nantes - Nantes Université - pôle Sociétés - Nantes Univ - Nantes Université)

Abstract

The elaboration of preference relations and their representations trace their source to early economic theory. Classical representations of preferences theorems rely on Debreu–Eilenberg's theorems in the topological setting. An important class of preferences consists of interval orders. A natural question is to achieve a bi-utility representation for interval orders. We suggest to introduce a condition reminiscent of N. Wiener's early works on the relativeness of positions. We obtain a bi-utility representation through the precedence and succession relations.

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  • Yann Rébillé, 2023. "A representation of interval orders through a bi-utility function," Post-Print hal-04785465, HAL.
    • Handle: RePEc:hal:journl:hal-04785465
    DOI: 10.1016/j.jmp.2023.102778
    Note: View the original document on HAL open archive server: https://hal.science/hal-04785465v1
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    References listed on IDEAS

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    1. Bridges, Douglas S., 1986. "Numerical representation of interval orders on a topological space," Journal of Economic Theory, Elsevier, vol. 38(1), pages 160-166, February.
    2. Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
    3. Peter C. Fishburn, 1970. "Intransitive Indifference in Preference Theory: A Survey," Operations Research, INFORMS, vol. 18(2), pages 207-228, April.
    4. Carlos Hervés‐Beloso & Hugo del Valle‐Inclán Cruces, 2019. "Continuous Preference Orderings Representable By Utility Functions," Journal of Economic Surveys, Wiley Blackwell, vol. 33(1), pages 179-194, February.
    5. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    6. Bridges, Douglas S., 1985. "Representing interval orders by a single real-valued function," Journal of Economic Theory, Elsevier, vol. 36(1), pages 149-155, June.
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