IDEAS home Printed from https://ideas.repec.org/a/kap/theord/v90y2021i1d10.1007_s11238-020-09774-0.html
   My bibliography  Save this article

Set and revealed preference axioms for multi-valued choice

Author

Listed:
  • Hans Peters

    (Maastricht University)

  • Panos Protopapas

    (University of Lausanne)

Abstract

We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant alternatives and so-called strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives.

Suggested Citation

  • Hans Peters & Panos Protopapas, 2021. "Set and revealed preference axioms for multi-valued choice," Theory and Decision, Springer, vol. 90(1), pages 11-29, February.
  • Handle: RePEc:kap:theord:v:90:y:2021:i:1:d:10.1007_s11238-020-09774-0
    DOI: 10.1007/s11238-020-09774-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11238-020-09774-0
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11238-020-09774-0?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. Walter Bossert & Hans Peters, 2009. "Single-peaked choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(2), pages 213-230, November.
    2. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Y. Ozbay, 2012. "Revealed Attention," American Economic Review, American Economic Association, vol. 102(5), pages 2183-2205, August.
    3. Echenique, Federico, 2007. "Counting combinatorial choice rules," Games and Economic Behavior, Elsevier, vol. 58(2), pages 231-245, February.
    4. Hugh Rose, 1958. "Consistency of Preference: The Two-Commodity Case," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 25(2), pages 124-125.
    5. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
    6. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    7. Johnson, Mark R. & Dean, Richard A., 2001. "Locally complete path independent choice functions and their lattices," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 53-87, July.
    8. Edith Elkind & Piotr Faliszewski & Piotr Skowron & Arkadii Slinko, 2017. "Properties of multiwinner voting rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 599-632, March.
    9. Alva, Samson, 2018. "WARP and combinatorial choice," Journal of Economic Theory, Elsevier, vol. 173(C), pages 320-333.
    10. Peters Hans & Wakker Peter, 1994. "WARP Does Not Imply SARP for More Than Two Commodities," Journal of Economic Theory, Elsevier, vol. 62(1), pages 152-160, February.
    11. Amartya K. Sen, 1971. "Choice Functions and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(3), pages 307-317.
    12. Brandt, Felix & Harrenstein, Paul, 2011. "Set-rationalizable choice and self-stability," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1721-1731, July.
    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. Bossert, Walter & Peters, Hans, 2019. "Choice on the simplex domain," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 63-72.
    2. Bossert, Walter, 1998. "Welfarism and rationalizability in allocation problems with indivisibilities1," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 133-150, March.
    3. Özgür Kıbrıs, 2012. "A revealed preference analysis of solutions to simple allocation problems," Theory and Decision, Springer, vol. 72(4), pages 509-523, April.
    4. Alva, Samson, 2018. "WARP and combinatorial choice," Journal of Economic Theory, Elsevier, vol. 173(C), pages 320-333.
    5. Christopher Tyson, 2013. "Behavioral implications of shortlisting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 941-963, October.
    6. Bossert, Walter, 1996. "The Kaldor compensation test and rational choice," Journal of Public Economics, Elsevier, vol. 59(2), pages 265-276, February.
    7. Walter Bossert & David Donaldson & Charles Blackorby, 1999. "Rationalizable solutions to pure population problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(3), pages 395-407.
    8. Christopher Tyson, 2013. "Behavioral implications of shortlisting procedures," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 941-963, October.
    9. Samson Alva & Battal Dou{g}an, 2021. "Choice and Market Design," Papers 2110.15446, arXiv.org, revised Nov 2021.
    10. Peters, Hans & Wakker, Peter, 1996. "Cycle-preserving extension of demand functions to new commodities," Journal of Mathematical Economics, Elsevier, vol. 25(3), pages 281-290.
    11. Walter Bossert & Hans Peters, 2009. "Single-peaked choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 41(2), pages 213-230, November.
    12. Tyson, Christopher J., 2008. "Cognitive constraints, contraction consistency, and the satisficing criterion," Journal of Economic Theory, Elsevier, vol. 138(1), pages 51-70, January.
    13. Tyson, Christopher J., 2008. "Cognitive constraints, contraction consistency, and the satisficing criterion," Journal of Economic Theory, Elsevier, vol. 138(1), pages 51-70, January.
    14. Domenico Cantone & Alfio Giarlotta & Stephen Watson, 2019. "Congruence relations on a choice space," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(2), pages 247-294, February.
    15. Ok, Efe A., 1998. "Inequality averse collective choice," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 301-321, October.
    16. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2020. "On the Structure of Stable Tournament Solutions," Papers 2004.01651, arXiv.org.
    17. Yongsheng Xu & Naoki Yoshihara, 2020. "Nonconvex Bargaining Problems: Some Recent Developments," Homo Oeconomicus: Journal of Behavioral and Institutional Economics, Springer, vol. 37(1), pages 7-41, November.
    18. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2018. "On the structure of stable tournament solutions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(2), pages 483-507, March.
    19. Özgür Kıbrıs, 2013. "On recursive solutions to simple allocation problems," Theory and Decision, Springer, vol. 75(3), pages 449-463, September.
    20. Ghosal, Sayantan & Dalton, Patricio, 2013. "Characterizing Behavioral Decisions with Choice Data," CAGE Online Working Paper Series 107, Competitive Advantage in the Global Economy (CAGE).

    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:kap:theord:v:90:y:2021:i:1:d:10.1007_s11238-020-09774-0. 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.