IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/102561.html
   My bibliography  Save this paper

On the Utility Function Representability of Lexicographic Preferences

Author

Listed:
  • Shi, Bowen
  • Wang, Gaowang
  • Zhang, Zhixiang

Abstract

The paper examines the utility function representability of the lexicographic preferences over multiple attributes. A sufficient and necessary condition is provided: a lexicographic preference is utility function representable if and only if there is at most one attribute with uncountable levels and when such an attribute exists, it is the least important one. An auxiliary result of independent interest for general rational preferences is proved stating that the class of utility function representable sets is closed in countable unions under some mild condition.

Suggested Citation

  • Shi, Bowen & Wang, Gaowang & Zhang, Zhixiang, 2020. "On the Utility Function Representability of Lexicographic Preferences," MPRA Paper 102561, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:102561
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/102561/1/MPRA_paper_102561.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Peter C. Fishburn, 1974. "Exceptional Paper--Lexicographic Orders, Utilities and Decision Rules: A Survey," Management Science, INFORMS, vol. 20(11), pages 1442-1471, July.
    2. Knoblauch, Vicki, 2000. "Lexicographic orders and preference representation," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 255-267, October.
    3. 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.
    4. Peter C. Fishburn, 1975. "Axioms for Lexicographic Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 42(3), pages 415-419.
    5. Bridges, Douglas S., 1983. "Numerical representation of intransitive preferences on a countable set," Journal of Economic Theory, Elsevier, vol. 30(1), pages 213-217, June.
    6. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    7. Bridges, Douglas S., 1983. "A numerical representation of preferences with intransitive indifference," Journal of Mathematical Economics, Elsevier, vol. 11(1), pages 25-42, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rajeev Kohli & Khaled Boughanmi & Vikram Kohli, 2019. "Randomized Algorithms for Lexicographic Inference," Operations Research, INFORMS, vol. 67(2), pages 357-375, March.
    2. Rajeev Kohli & Kamel Jedidi, 2007. "Representation and Inference of Lexicographic Preference Models and Their Variants," Marketing Science, INFORMS, vol. 26(3), pages 380-399, 05-06.
    3. Begoña Subiza Martínez & Carmen Herrero Blanco, 1991. "A characterization of acyclic preferences on countable sets," Working Papers. Serie AD 1991-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    4. Knoblauch, Vicki, 2000. "Lexicographic orders and preference representation," Journal of Mathematical Economics, Elsevier, vol. 34(2), pages 255-267, October.
    5. Estévez Toranzo, Margarita & Hervés Beloso, Carlos & López López, Miguel A., 1993. "Una nota sobre la representación numérica de relaciones de preferencia," DES - Documentos de Trabajo. Estadística y Econometría. DS 2941, Universidad Carlos III de Madrid. Departamento de Estadística.
    6. Begoña Subiza Martínez, 1993. "Numerical Representation Of Acyclic Preferences," Working Papers. Serie AD 1993-09, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    7. Petri, Henrik & Voorneveld, Mark, 2016. "Characterizing lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 54-61.
    8. Angilella, Silvia & Giarlotta, Alfio, 2009. "Implementations of PACMAN," European Journal of Operational Research, Elsevier, vol. 194(2), pages 474-495, April.
    9. Toranzo, Margarita Estevez & Garcia-Cutrin, Javier & Lopez Lopez, Miguel A., 1995. "A note on the representation of preferences," Mathematical Social Sciences, Elsevier, vol. 29(3), pages 255-262, June.
    10. Marc-Arthur Diaye & Michal Wong-Urdanivia, 2005. "A simple test of Richter-rationality," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00084390, HAL.
    11. Mitra, Manipushpak & Sen, Debapriya, 2014. "An alternative proof of Fishburn’s axiomatization of lexicographic preferences," Economics Letters, Elsevier, vol. 124(2), pages 168-170.
    12. Marc-Arthur Diaye & Michal Wong-Urdanivia, 2005. "A simple test of Richter-rationality," Post-Print halshs-00084390, HAL.
    13. Michael Mandler, 2021. "The lexicographic method in preference theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 553-577, March.
    14. Marc-Arthur Diaye & Michal Wong-Urdanivia, 2006. "A Simple Test of Richter-Rationality," Documents de recherche 06-01, Centre d'Études des Politiques Économiques (EPEE), Université d'Evry Val d'Essonne.
    15. 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.
    16. Bosi, Gianni & Isler, Romano, 1995. "Representing preferences with nontransitive indifference by a single real-valued function," Journal of Mathematical Economics, Elsevier, vol. 24(7), pages 621-631.
    17. Hougaard, Jens Leth & Tvede, Mich, 2001. "The existence of maximal elements: generalized lexicographic relations," Journal of Mathematical Economics, Elsevier, vol. 36(2), pages 111-115, November.
    18. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2019. "The Ordinal Input for Cardinal Output Approach of Non-compensatory Composite Indicators: The PROMETHEE Scoring Method," MPRA Paper 95816, University Library of Munich, Germany.
    19. Greco, Salvatore & Ishizaka, Alessio & Tasiou, Menelaos & Torrisi, Gianpiero, 2021. "The ordinal input for cardinal output approach of non-compensatory composite indicators: the PROMETHEE scoring method," European Journal of Operational Research, Elsevier, vol. 288(1), pages 225-246.
    20. Knoblauch, Vicki, 2005. "Continuous lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 41(7), pages 812-825, November.

    More about this item

    Keywords

    Lexicographic Preference; Utility Function Representation; Representable Class; Pseudo-continuous Points;
    All these keywords.

    JEL classification:

    • D0 - Microeconomics - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:102561. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.