[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v84y2019icp63-72.html
   My bibliography  Save this article

Choice on the simplex domain

Author

Listed:
  • Bossert, Walter
  • Peters, Hans
Abstract
One unit of a good has to be divided among a group of agents who each are entitled to a minimal share, and these shares sum up to less than one. The associated set of choice problems consists of the unit simplex and all its full-dimensional subsimplices with the same orientation. We characterize all choice rules that are independent of irrelevant alternatives, continuous, and monotonic; the last condition means that if an agent receives its minimal share and that share increases, then no other agent benefits. In line with Kıbrıs (2012) we show that these rules are rationalizable and representable by a real-valued function. On the issue of rationalizability, we also consider weakenings of our conditions. In particular, we show that in general, excluding cycles of any fixed length does not imply the strong axiom of revealed preference, that is, the exclusion of cycles of any length. For continuous three-agent choice rules, however, excluding cycles of length three implies the strong axiom of revealed preference.

Suggested Citation

  • Bossert, Walter & Peters, Hans, 2019. "Choice on the simplex domain," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 63-72.
    • Handle: RePEc:eee:mateco:v:84:y:2019:i:c:p:63-72
    DOI: 10.1016/j.jmateco.2019.07.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406819300758
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2019.07.002?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. 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. Stovall, John E., 2014. "Collective rationality and monotone path division rules," Journal of Economic Theory, Elsevier, vol. 154(C), pages 1-24.
    3. Bossert, Walter, 1994. "Rational choice and two-person bargaining solutions," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 549-563, November.
    4. Bossert, Walter & Suzumura, Kotaro, 2010. "Consistency, Choice, and Rationality," Economics Books, Harvard University Press, number 9780674052994, Spring.
    5. Blackorby, Charles & Bossert, Walter & Donaldson, David, 1995. "Multi-valued demand and rational choice in the two-commodity case," Economics Letters, Elsevier, vol. 47(1), pages 5-10, January.
    6. 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.
    7. Peters, Hans & Wakker, Peter, 1991. "Independence of Irrelevant Alternatives and Revealed Group Preferences," Econometrica, Econometric Society, vol. 59(6), pages 1787-1801, November.
    8. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    9. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    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. Özgür Kıbrıs, 2012. "A revealed preference analysis of solutions to simple allocation problems," Theory and Decision, Springer, vol. 72(4), pages 509-523, April.
    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, 1998. "Welfarism and rationalizability in allocation problems with indivisibilities1," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 133-150, March.
    2. Özgür Kıbrıs, 2012. "A revealed preference analysis of solutions to simple allocation problems," Theory and Decision, Springer, vol. 72(4), pages 509-523, April.
    3. 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.
    4. 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.
    5. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    6. 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.
    7. Bossert, Walter, 1996. "The Kaldor compensation test and rational choice," Journal of Public Economics, Elsevier, vol. 59(2), pages 265-276, February.
    8. Ok, Efe A., 1998. "Inequality averse collective choice," Journal of Mathematical Economics, Elsevier, vol. 30(3), pages 301-321, October.
    9. 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.
    10. Bossert, Walter & Peters, Hans, 2013. "Single-plateaued choice," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 134-139.
    11. Marco Mariotii, 1996. "Fair bargains: distributive justice and Nash Bargaining Theory," Game Theory and Information 9611003, University Library of Munich, Germany, revised 06 Dec 1996.
    12. Bossert, Walter & Peters, Hans, 2014. "Single-basined choice," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 162-168.
    13. Stovall, John E., 2014. "Collective rationality and monotone path division rules," Journal of Economic Theory, Elsevier, vol. 154(C), pages 1-24.
    14. 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.
    15. Flores-Szwagrzak, Karol, 2015. "Priority classes and weighted constrained equal awards rules for the claims problem," Journal of Economic Theory, Elsevier, vol. 160(C), pages 36-55.
    16. Stovall, John E., 2020. "Equal sacrifice taxation," Games and Economic Behavior, Elsevier, vol. 121(C), pages 55-75.
    17. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    18. Özgür Kıbrıs, 2013. "On recursive solutions to simple allocation problems," Theory and Decision, Springer, vol. 75(3), pages 449-463, September.
    19. Wulf Gaertner & Richard Bradley & Yongsheng Xu & Lars Schwettmann, 2019. "Against the proportionality principle: Experimental findings on bargaining over losses," PLOS ONE, Public Library of Science, vol. 14(7), pages 1-18, July.
    20. Cherchye, Laurens & Demuynck, Thomas & De Rock, Bram, 2018. "Transitivity of preferences: when does it matter?," Theoretical Economics, Econometric Society, vol. 13(3), September.

    More about this item

    Keywords

    Choice rules; Simplex domain; Rationalizability; Representability;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

    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:eee:mateco:v:84:y:2019:i:c:p:63-72. 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.