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Numerical Representations of Imperfectly Ordered Preferences (A Unified Geometric Exposition

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  • Avraham Beja
  • Itzhak Gilboa

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
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Suggested Citation

  • 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.
    • Handle: RePEc:nwu:cmsems:836
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    Cited by:

    1. 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.
    2. Denis Bouyssou & Marc Pirlot, 2021. "Unit representation of semiorders I: Countable sets," Post-Print hal-02918005, HAL.
    3. 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.
    4. Pawel Dziewulski, 2016. "Eliciting the just-noticeable difference," Economics Series Working Papers 798, University of Oxford, Department of Economics.
    5. Denis Bouyssou & Marc Pirlot, 2020. "Unit representation of semiorders I: Countable sets," Working Papers hal-02918005, HAL.
    6. Dziewulski, Paweł, 2020. "Just-noticeable difference as a behavioural foundation of the critical cost-efficiency index," Journal of Economic Theory, Elsevier, vol. 188(C).
    7. Argenziano, Rossella & Gilboa, Itzhak, 2017. "Psychophysical foundations of the Cobb–Douglas utility function," Economics Letters, Elsevier, vol. 157(C), pages 21-23.
    8. Denis Bouyssou & Marc Pirlot, 2021. "Unit representation of semiorders II: The general case," Post-Print hal-02918017, HAL.
    9. Pawel Dziewulski, 2021. "A comprehensive revealed preference approach to approximate utility maximisation," Working Paper Series 0621, Department of Economics, University of Sussex Business School.
    10. 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.
    11. Xiaosheng Mu, 2021. "Sequential Choice with Incomplete Preferences," Working Papers 2021-35, Princeton University. Economics Department..
    12. Denis Bouyssou & Marc Pirlot, 2020. "Unit representation of semiorders II: The general case," Working Papers hal-02918017, HAL.
    13. 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.
    14. Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    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.
    16. Xiaosheng Mu, 2019. "Amendment Voting with Incomplete Preferences," Working Papers 2019-29, Princeton University. Economics Department..
    17. 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.

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