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Numerical representations of imperfectly ordered preferences (a unified geometric exposition)

Author

Listed:
  • Itzhak Gilboa

    (Northwestern University [Evanston])

  • Avraham Beja

    (TAU - Tel Aviv University)

Abstract

This paper uses "generalized numerical representations" to extend some of the result of utility theory regarding imperfectly ordered preferences in general and semiordered preferences in particular. It offers a unified geometric approach, which helps visualize how the increasingly stringent conditions of suborders, interval orders, semiorders, and weak orders give rise to increasingly intuitive representations. The differences between the proposed framework and the more traditional utility representations are especially significant in the context of uncountable sets

Suggested Citation

  • Itzhak Gilboa & Avraham Beja, 1992. "Numerical representations of imperfectly ordered preferences (a unified geometric exposition)," Post-Print hal-00481383, HAL.
    • Handle: RePEc:hal:journl:hal-00481383
    DOI: 10.1016/0022-2496(92)90030-B
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    Citations

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    Cited by:

    1. Gilboa, Itzhak & Lapson, Robert, 1995. "Aggregation of Semiorders: Intransitive Indifference Makes a Difference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 109-126, January.
    2. Denis Bouyssou & Marc Pirlot, 2020. "Unit representation of semiorders I: Countable sets," Working Papers hal-02918005, HAL.
    3. Dziewulski, Paweł, 2020. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency index," Journal of Economic Theory, Elsevier, vol. 188(C).
    4. Argenziano, Rossella & Gilboa, Itzhak, 2017. "Psychophysical foundations of the Cobb–Douglas utility function," Economics Letters, Elsevier, vol. 157(C), pages 21-23.
    5. Denis Bouyssou & Marc Pirlot, 2020. "Unit representation of semiorders II: The general case," Working Papers hal-02918017, HAL.
    6. Pawel Dziewulski, 2016. "Eliciting the just-noticeable difference," Economics Series Working Papers 798, University of Oxford, Department of Economics.
    7. Pawel Dziewulski, 2021. "A comprehensive revealed preference approach to approximate utility maximisation," Working Paper Series 0621, Department of Economics, University of Sussex Business School.
    8. Xiaosheng Mu, 2019. "Amendment Voting with Incomplete Preferences," Working Papers 2019-29, Princeton University. Economics Department..
    9. Pawel Dziewulski, 2018. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency," Economics Series Working Papers 848, University of Oxford, Department of Economics.
    10. Leobardo Plata-Perez, 2004. "A numerical representation of acyclic preferences when non-comparability and indifference are concepts with different meaning," EconoQuantum, Revista de Economia y Finanzas, Universidad de Guadalajara, Centro Universitario de Ciencias Economico Administrativas, Departamento de Metodos Cuantitativos y Maestria en Economia., vol. 1(0), pages 17-23, Enero - J.
    11. Abrísqueta, Francisco J. & Candeal, Juan C. & Induráin, Esteban & Zudaire, Margarita, 2009. "Scott-Suppes representability of semiorders: Internal conditions," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 245-261, March.
    12. Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    13. 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.
    14. Xiaosheng Mu, 2021. "Sequential Choice with Incomplete Preferences," Working Papers 2021-35, Princeton University. Economics Department..
    15. Alejandro Islas-Camargo & Willy W. Cortez, 2004. "Convergencia salarial entre las principales ciudades mexicanas: Un analisis de cointegracion," EconoQuantum, Revista de Economia y Finanzas, Universidad de Guadalajara, Centro Universitario de Ciencias Economico Administrativas, Departamento de Metodos Cuantitativos y Maestria en Economia., vol. 1(0), pages 25-47, Enero - J.

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