IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v45y2015i1p51-69.html
   My bibliography  Save this article

Hyper-relations, choice functions, and orderings of opportunity sets

Author

Listed:
  • V. Danilov
  • G. Koshevoy
  • E. Savaglio

Abstract

We prove a coincidence of the class of multi-preference hyper-relations and the class of decent hyper-relations (DHR), that is the class of binary relations on opportunity sets satisfying monotonicity, no-dummy, stability with respect to contraction and extension, and the union property. We study subclasses of DHR. In order to pursue our analysis, we establish a canonical bijection between DHR and the class of no-dummy heritage choice functions. From this we obtain that the no-dummy heritage choice functions have multi-criteria rationalizations with reflexive binary relations. We also prove that the restriction of this bijection to two subclasses of DHR, namely the transitive decent hyper-relations, and the ample hyper-relations, is a bijection between these subclasses and the classes of closed no-dummy choice functions and no-dummy path-independent choice functions (Plott functions), respectively. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • V. Danilov & G. Koshevoy & E. Savaglio, 2015. "Hyper-relations, choice functions, and orderings of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(1), pages 51-69, June.
    • Handle: RePEc:spr:sochwe:v:45:y:2015:i:1:p:51-69
    DOI: 10.1007/s00355-014-0844-5
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00355-014-0844-5
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00355-014-0844-5?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. Puppe, Clemens, 1996. "An Axiomatic Approach to "Preference for Freedom of Choice"," Journal of Economic Theory, Elsevier, vol. 68(1), pages 174-199, January.
    2. Kreps, David M, 1979. "A Representation Theorem for "Preference for Flexibility"," Econometrica, Econometric Society, vol. 47(3), pages 565-577, May.
    3. Domenach, Florent & Leclerc, Bruno, 2004. "Closure systems, implicational systems, overhanging relations and the case of hierarchical classification," Mathematical Social Sciences, Elsevier, vol. 47(3), pages 349-366, May.
    4. Matthew Ryan, 2014. "Path independent choice and the ranking of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 193-213, January.
    5. Danilov, V. & Koshevoy, G., 2005. "Mathematics of Plott choice functions," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 245-272, May.
    6. Somdeb Lahiri, 2003. "Justifiable preferences over opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 117-129, August.
    7. Prasanta K. PATTANAIK & Yongsheng XU, 1990. "On Ranking Opportunity Sets in Terms of Freedom of Choice," Discussion Papers (REL - Recherches Economiques de Louvain) 1990036, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    8. Caspard, N. & Monjardet, B., 2000. "The Lattice of Closure Systems, Closure Operators and Implicational Systems on a Finite Set : A Survey," Papiers d'Economie Mathématique et Applications 2000.120, Université Panthéon-Sorbonne (Paris 1).
    9. Clemens Puppe & Yongsheng Xu, 2010. "Essential alternatives and freedom rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 669-685, October.
    10. Danilov, V. & Koshevoy, G., 2006. "A new characterization of the path independent choice functions," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 238-245, March.
    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. Matthew Ryan, 2016. "Essentiality and Convexity in the Ranking of Opportunity Sets," Working Papers 2016-01, Auckland University of Technology, Department of Economics.
    2. Matthew Ryan, 2016. "Essentiality and convexity in the ranking of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 853-877, December.
    3. Koshevoy, Gleb & Savaglio, Ernesto, 2023. "On rational choice from lists of sets," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    4. Gleb Koshevoy & Ernesto Savaglio, 2017. "Enveloped choice functions and path-independent rationality," Department of Economics University of Siena 765, Department of Economics, University of Siena.
    5. Alfio Giarlotta & Angelo Petralia & Stephen Watson, 2022. "Semantics meets attractiveness: Choice by salience," Papers 2204.08798, arXiv.org, revised Aug 2022.

    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. 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.
    2. Vladimir Danilov & Gleb Koshevoy & Ernesto Savaglio, 2012. "Orderings of Opportunity Sets," Working Papers 282, ECINEQ, Society for the Study of Economic Inequality.
    3. Matthew Ryan, 2016. "Essentiality and convexity in the ranking of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 853-877, December.
    4. Matthew Ryan, 2016. "Essentiality and Convexity in the Ranking of Opportunity Sets," Working Papers 2016-01, Auckland University of Technology, Department of Economics.
    5. Matthew Ryan, 2014. "Path independent choice and the ranking of opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(1), pages 193-213, January.
    6. 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.
    7. 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.
    8. Prasanta Pattanaik & Yongsheng Xu, 1998. "On Preference and Freedom," Theory and Decision, Springer, vol. 44(2), pages 173-198, April.
    9. Walter Bossert, 1998. "Opportunity Sets and the Measurement of Information," Discussion Papers 98/6, University of Nottingham, School of Economics.
    10. Rommeswinkel, Hendrik, 2011. "Measuring Freedom in Games," MPRA Paper 106426, University Library of Munich, Germany, revised 03 Mar 2021.
    11. Somdeb Lahiri, 2018. "Indirect Utility Reflecting Anxiety and Flexibility of Choice," Journal of Economics and Management, College of Business, Feng Chia University, Taiwan, vol. 14(1), pages 33-50, February.
    12. Bossert, Walter, 2000. "Opportunity sets and uncertain consequences1," Journal of Mathematical Economics, Elsevier, vol. 33(4), pages 475-496, May.
    13. Dan Qin, 2015. "On justifiable choice functions over opportunity sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 269-285, September.
    14. Ricardo Arlegi, 1998. "Incomplete Preferences and The Preference for Flexibility," Documentos de Trabajo - Lan Gaiak Departamento de Economía - Universidad Pública de Navarra 9819, Departamento de Economía - Universidad Pública de Navarra.
    15. Ballester, Miguel A. & de Miguel, Juan R. & Nieto, Jorge, 2004. "Set comparisons in a general domain: the Indirect Utility Criterion," Mathematical Social Sciences, Elsevier, vol. 48(2), pages 139-150, September.
    16. Falkinger, Josef, 2016. "The order of knowledge and robust action: How to deal with economic uncertainty?," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 10, pages 1-30.
    17. Klaus Nehring, 2003. "Preference for Flexibility and Freedom of Choice in a Savage Framework," Working Papers 51, University of California, Davis, Department of Economics.
    18. Baharad, Eyal & Nitzan, Shmuel, 2003. "Essential alternatives and set-dependent preferences--an axiomatic approach," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 121-129, April.
    19. Martin Hees, 2010. "The specific value of freedom," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 687-703, October.
    20. Eckehard F. Rosenbaum, 2000. "On Measuring Freedom," Journal of Theoretical Politics, , vol. 12(2), pages 205-227, April.

    More about this item

    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:sochwe:v:45:y:2015:i:1:p:51-69. 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.