IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v67y2016icp32-37.html
   My bibliography  Save this article

Canonical utility functions and continuous preference extensions

Author

Listed:
  • Kopylov, Igor

Abstract

I define canonical utility functions via an explicit formula that inherits semicontinuity, continuity, Cauchy continuity, and uniform continuity from preferences. This construction is used to (i)show Rader’s and Debreu’s theorems in a fast and transparent way,(ii)refine these results for Cauchy and uniformly continuous preferences on a metric space X,(iii)extend such preferences from X to any larger metric domain Y⊃X, while preserving Cauchy and uniform continuity respectively. By contrast, regular continuity does not guarantee that continuous preference extensions should exist even in standard decision theoretic frameworks. For example, continuous preferences over simple lotteries or finite menus need not have continuous extensions to Borel distributions or compact menus respectively.

Suggested Citation

  • Kopylov, Igor, 2016. "Canonical utility functions and continuous preference extensions," Journal of Mathematical Economics, Elsevier, vol. 67(C), pages 32-37.
    • Handle: RePEc:eee:mateco:v:67:y:2016:i:c:p:32-37
    DOI: 10.1016/j.jmateco.2016.08.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406816301100
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2016.08.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Herden, G., 1989. "On the existence of utility functions," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 297-313, June.
    2. Herden, G., 1989. "On the existence of utility functions ii," Mathematical Social Sciences, Elsevier, vol. 18(2), pages 107-117, October.
    3. Kopylov, Igor, 2010. "Unbounded probabilistic sophistication," Mathematical Social Sciences, Elsevier, vol. 60(2), pages 113-118, September.
    4. Yi, Gyoseob, 1993. "Continuous extension of preferences," Journal of Mathematical Economics, Elsevier, vol. 22(6), pages 547-555.
    5. Jaffray, Jean-Yves, 1975. "Existence of a Continuous Utility Function: An Elementary Proof," Econometrica, Econometric Society, vol. 43(5-6), pages 981-983, Sept.-Nov.
    6. Mehta, Ghanshyam, 1977. "Topological Ordered Spaces and Utility Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 779-782, October.
    7. Özgür Evren & Stefania Minardi, 2017. "Warm‐glow Giving and Freedom to be Selfish," Economic Journal, Royal Economic Society, vol. 127(603), pages 1381-1409, August.
    8. Paolo Ghirardato & Marciano Siniscalchi, 2012. "Ambiguity in the Small and in the Large," Econometrica, Econometric Society, vol. 80(6), pages 2827-2847, November.
    9. Trout Rader, 1963. "The Existence of a Utility Function to Represent Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 30(3), pages 229-232.
    10. Wakker, Peter & Erev, Ido & Weber, Elke U, 1994. "Comonotonic Independence: The Critical Test between Classical and Rank-Dependent Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 9(3), pages 195-230, December.
    11. Faruk Gul & Wolfgang Pesendorfer, 2001. "Temptation and Self-Control," Econometrica, Econometric Society, vol. 69(6), pages 1403-1435, November.
    12. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
    13. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    14. Kopylov, Igor, 2010. "Simple axioms for countably additive subjective probability," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 867-876, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Özgür Evren, 2017. "Cautious and Globally Ambiguity Averse," Working Papers w0236, Center for Economic and Financial Research (CEFIR).
    2. Uyanik, Metin & Khan, M. Ali, 2022. "The continuity postulate in economic theory: A deconstruction and an integration," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    3. Evren, Özgür, 2019. "Recursive non-expected utility: Connecting ambiguity attitudes to risk preferences and the level of ambiguity," Games and Economic Behavior, Elsevier, vol. 114(C), pages 285-307.

    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. Yann Rébillé, 2019. "Continuous utility on connected separable topological spaces," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(1), pages 147-153, May.
    2. Bosi, G. & Mehta, G. B., 2002. "Existence of a semicontinuous or continuous utility function: a unified approach and an elementary proof," Journal of Mathematical Economics, Elsevier, vol. 38(3), pages 311-328, November.
    3. Carlos Alós-Ferrer & Klaus Ritzberger, 2015. "On the characterization of preference continuity by chains of sets," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(2), pages 115-128, October.
    4. Athanasios Andrikopoulos, 2011. "Characterization of the existence of semicontinuous weak utilities for binary relations," Theory and Decision, Springer, vol. 70(1), pages 13-26, January.
    5. Pivato, Marcus, 2009. "Social choice with approximate interpersonal comparisons of well-being," MPRA Paper 17060, University Library of Munich, Germany.
    6. Bosi, Gianni & Zuanon, Magali E., 2003. "Continuous representability of homothetic preorders by means of sublinear order-preserving functions," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 333-341, July.
    7. 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.
    8. Mihm, Maximilian & Ozbek, Kemal, 2019. "On the identification of changing tastes," Games and Economic Behavior, Elsevier, vol. 116(C), pages 203-216.
    9. Pedro Hack & Daniel A. Braun & Sebastian Gottwald, 2022. "Representing preorders with injective monotones," Theory and Decision, Springer, vol. 93(4), pages 663-690, November.
    10. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
    11. Alcantud, J. C. R. & Rodriguez-Palmero, C., 1999. "Characterization of the existence of semicontinuous weak utilities," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 503-509, December.
    12. Herden, G., 1995. "On some equivalent approaches to Mathematical Utility Theory," Mathematical Social Sciences, Elsevier, vol. 29(1), pages 19-31, February.
    13. Nosratabadi, Hassan, 2014. "Partially upper continuous preferences: Representation and maximal elements," Economics Letters, Elsevier, vol. 125(3), pages 408-410.
    14. Yosuke Hashidate & Tetsuya Kawamura & Fabrice Le Lec & Yusuke Osaki & Benoît Tarroux, 2024. "Impure motivations in social preferences: Experimental evidence from menu choices," Working Papers 2406, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    15. Thunström, Linda & Nordström, Jonas & Shogren, Jason F., 2015. "Certainty and overconfidence in future preferences for food," Journal of Economic Psychology, Elsevier, vol. 51(C), pages 101-113.
    16. André Lapied & Thomas Rongiconi, 2013. "Ambiguity as a Source of Temptation: Modeling Unstable Beliefs," Working Papers halshs-00797631, HAL.
    17. Eddie Dekel & Barton L. Lipman & Aldo Rustichini, 2009. "Temptation-Driven Preferences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 76(3), pages 937-971.
    18. Andreoni, James & Serra-Garcia, Marta, 2021. "Time inconsistent charitable giving," Journal of Public Economics, Elsevier, vol. 198(C).
    19. Bryan, Gharad & Karlan, Dean & Nelson, Scott, 2009. "Commitment Contracts," Working Papers 73, Yale University, Department of Economics.
    20. Lefgren, Lars J. & Stoddard, Olga B. & Stovall, John E., 2021. "Rationalizing self-defeating behaviors: Theory and evidence," Journal of Health Economics, Elsevier, vol. 76(C).

    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:eee:mateco:v:67:y:2016:i:c:p:32-37. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    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.