IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v63y2017i1d10.1007_s00199-015-0942-3.html
   My bibliography  Save this article

Infinite supermodularity and preferences

Author

Listed:
  • Alain Chateauneuf

    (Paris School of Economics and University of Paris I)

  • Vassili Vergopoulos

    (Paris School of Economics and University of Paris I)

  • Jianbo Zhang

    (University of Kansas)

Abstract

Chambers and Echenique (J Econ Theory 144:1004–1014, 2009) proved that preferences in a wide class cannot disentangle the usual economic assumptions of quasisupermodularity and supermodularity. This paper further studies the ordinal content of the much stronger assumption of infinite supermodularity in the same context. It is shown that weakly increasing binary relations on finite lattices fail to disentangle infinite supermodularity from quasisupermodularity and supermodularity. Moreover, for a complete preorder, the mild requirement of strict increasingness is shown to imply the existence of infinitely supermodular representations.

Suggested Citation

  • Alain Chateauneuf & Vassili Vergopoulos & Jianbo Zhang, 2017. "Infinite supermodularity and preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 99-109, January.
    • Handle: RePEc:spr:joecth:v:63:y:2017:i:1:d:10.1007_s00199-015-0942-3
    DOI: 10.1007/s00199-015-0942-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-015-0942-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-015-0942-3?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    2. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    3. Chambers, Christopher P. & Echenique, Federico, 2009. "Supermodularity and preferences," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1004-1014, May.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    5. Klaus Nehring & Clemens Puppe, 2002. "A Theory of Diversity," Econometrica, Econometric Society, vol. 70(3), pages 1155-1198, May.
    6. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    7. Chambers, Christopher P. & Echenique, Federico, 2008. "Ordinal notions of submodularity," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1243-1245, December.
    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. Brian Duricy, 2023. "Preferences on Ranked-Choice Ballots," Papers 2301.02697, arXiv.org.

    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. Brian Duricy, 2023. "Preferences on Ranked-Choice Ballots," Papers 2301.02697, arXiv.org.
    2. Evan Piermont, 2021. "Hypothetical Expected Utility," Papers 2106.15979, arXiv.org, revised Jul 2021.
    3. André Lapied & Thomas Rongiconi, 2013. "Ambiguity as a Source of Temptation: Modeling Unstable Beliefs," Working Papers halshs-00797631, HAL.
    4. Chambers, Christopher P. & Miller, Alan D. & Yenmez, M. Bumin, 2020. "Closure and preferences," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 161-166.
    5. Vassili Vergopoulos, 2014. "A Behavioral Definition of States of the World," Documents de travail du Centre d'Economie de la Sorbonne 14047, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Jewitt, Ian & Mukerji, Sujoy, 2017. "Ordering ambiguous acts," Journal of Economic Theory, Elsevier, vol. 171(C), pages 213-267.
    7. Barbera, S. & Bossert, W. & Pattanaik, P.K., 2001. "Ranking Sets of Objects," Cahiers de recherche 2001-02, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    8. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    9. Gajdos, T. & Hayashi, T. & Tallon, J.-M. & Vergnaud, J.-C., 2008. "Attitude toward imprecise information," Journal of Economic Theory, Elsevier, vol. 140(1), pages 27-65, May.
    10. Yehuda Izhakian, 2012. "Ambiguity Measurement," Working Papers 12-01, New York University, Leonard N. Stern School of Business, Department of Economics.
    11. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2009. "A characterization of the 2-additive Choquet integral through cardinal information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445132, HAL.
    12. Klaus Nehring, 2003. "Preference for Flexibility and Freedom of Choice in a Savage Framework," Working Papers 51, University of California, Davis, Department of Economics.
    13. Takao Asano & Hiroyuki Kojima, 2022. "Choquet Integrals and Belief Functions," KIER Working Papers 1077, Kyoto University, Institute of Economic Research.
    14. Antoinette Baujard, 2006. "Conceptions of freedom and ranking opportunity sets. A typology," Economics Working Paper Archive (University of Rennes & University of Caen) 200611, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    15. Alain Chateauneuf & Thibault Gajdos & Jean-Yves Jaffray, 2011. "Regular updating," Theory and Decision, Springer, vol. 71(1), pages 111-128, July.
    16. Takao Asano & Hiroyuki Kojima, 2013. "An Axiomatization of Choquet Expected Utility with Cominimum Independence," KIER Working Papers 878, Kyoto University, Institute of Economic Research.
    17. Peter Wakker, 2011. "Jaffray’s ideas on ambiguity," Theory and Decision, Springer, vol. 71(1), pages 11-22, July.
    18. Jimena Galindo & Levent Ülkü, 2020. "Diversity relations over menus," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 229-242, August.
    19. Hamed Hamze Bajgiran & Federico Echenique, 2022. "Closure operators: Complexity and applications to classification and decision-making," Papers 2202.05339, arXiv.org, revised May 2022.
    20. Kunimoto, Takashi & Yamashita, Takuro, 2020. "Order on types based on monotone comparative statics," Journal of Economic Theory, Elsevier, vol. 189(C).

    More about this item

    Keywords

    Supermodularity; Infinite supermodularity; Lattice;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

    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:spr:joecth:v:63:y:2017:i:1:d:10.1007_s00199-015-0942-3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.