IDEAS home Printed from https://ideas.repec.org/p/ris/qmetal/2015_005.html
   My bibliography  Save this paper

Rationalizable Choice and Standards of Behavior

Author

Listed:
  • Josep E., Peris

    (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

  • Begoña, Subiza

    (Universidad de Alicante, Departamento de Métodos Cuantitativos y Teoría Económica)

Abstract

Two independent approaches have been used in order to analyze individual or collective choices. A prominent notion is rationality: individuals choose alternatives maximizing binary relations. This natural property turns out to be problematic, especially in social choice, and gives rise to the well-known Arrow's impossibility result. A different analysis is to observe choices in terms of standards of behavior, as proposed by von Neumann and Morgenstern 1944) with the notion of stable sets. Although stability seems a desirable property to be fulfilled by any choice function, the usual choice functions in tournaments (top cycle, uncovered set, minimal covering,...) do not fulfill it. We introduce a new stability concept (v-stability) that in turn extends the notion of rationality. We prove that the usual tournament choice functions fulfill this new stability condition.

Suggested Citation

  • Josep E., Peris & Begoña, Subiza, 2015. "Rationalizable Choice and Standards of Behavior," QM&ET Working Papers 15-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    • Handle: RePEc:ris:qmetal:2015_005
    as

    Download full text from publisher

    File URL: http://web.ua.es/es/dmcte/documentos/qmetwp1505.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Brandt, Felix, 2011. "Minimal stable sets in tournaments," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1481-1499, July.
    2. Peris, Josep E. & Subiza, Begoña, 2013. "A reformulation of von Neumann–Morgenstern stability: m-stability," Mathematical Social Sciences, Elsevier, vol. 66(1), pages 51-55.
    3. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
    4. Matsuyama, Kiminori, 1985. "Chernoff's dual axiom, revealed preference and weak rational choice functions," Journal of Economic Theory, Elsevier, vol. 35(1), pages 155-165, February.
    5. Begoña Subiza & Josep Peris, 2000. "Choice Functions: Rationality re-Examined," Theory and Decision, Springer, vol. 48(3), pages 287-304, May.
    6. Deb, Rajat, 1983. "Binariness and rational choice," Mathematical Social Sciences, Elsevier, vol. 5(1), pages 97-105, August.
    7. Laffond G. & Laslier J. F. & Le Breton M., 1993. "The Bipartisan Set of a Tournament Game," Games and Economic Behavior, Elsevier, vol. 5(1), pages 182-201, January.
    8. John C. Harsanyi, 1974. "An Equilibrium-Point Interpretation of Stable Sets and a Proposed Alternative Definition," Management Science, INFORMS, vol. 20(11), pages 1472-1495, July.
    9. Dutta, Bhaskar, 1988. "Covering sets and a new condorcet choice correspondence," Journal of Economic Theory, Elsevier, vol. 44(1), pages 63-80, February.
    10. 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. Josep E. Peris & Begoña Subiza, 2023. "Rational stability of choice functions," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(3), pages 580-598, September.
    2. 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.
    3. Brandt, Felix & Harrenstein, Paul & Seedig, Hans Georg, 2017. "Minimal extending sets in tournaments," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 55-63.
    4. Felix Brandt & Markus Brill & Hans Georg Seedig & Warut Suksompong, 2020. "On the Structure of Stable Tournament Solutions," Papers 2004.01651, arXiv.org.
    5. Felix Brandt & Markus Brill & Felix Fischer & Paul Harrenstein, 2014. "Minimal retentive sets in tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(3), pages 551-574, March.
    6. Aleksei Y. Kondratev & Vladimir V. Mazalov, 2020. "Tournament solutions based on cooperative game theory," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 119-145, March.
    7. Weibin Han & Adrian Deemen, 2019. "A refinement of the uncovered set in tournaments," Theory and Decision, Springer, vol. 86(1), pages 107-121, February.
    8. Begoña Subiza & Josep Peris, 2000. "Choice Functions: Rationality re-Examined," Theory and Decision, Springer, vol. 48(3), pages 287-304, May.
    9. Felix Brandt, 2015. "Set-monotonicity implies Kelly-strategyproofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(4), pages 793-804, December.
    10. Brandt, Felix & Harrenstein, Paul, 2011. "Set-rationalizable choice and self-stability," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1721-1731, July.
    11. De Donder, Philippe & Le Breton, Michel & Truchon, Michel, 2000. "Choosing from a weighted tournament1," Mathematical Social Sciences, Elsevier, vol. 40(1), pages 85-109, July.
    12. Banks, Jeffrey S. & Duggan, John & Le Breton, Michel, 2002. "Bounds for Mixed Strategy Equilibria and the Spatial Model of Elections," Journal of Economic Theory, Elsevier, vol. 103(1), pages 88-105, March.
    13. Borm, Peter & van den Brink, Rene & Levinsky, Rene & Slikker, Marco, 2004. "On two new social choice correspondences," Mathematical Social Sciences, Elsevier, vol. 47(1), pages 51-68, January.
    14. Daniel R. Carroll & Jim Dolmas & Eric Young, 2015. "Majority Voting: A Quantitative Investigation," Working Papers (Old Series) 1442, Federal Reserve Bank of Cleveland.
    15. Vincent Anesi, 2012. "A new old solution for weak tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(4), pages 919-930, October.
    16. Page Jr., Frank H. & Wooders, Myrna, 2009. "Strategic basins of attraction, the path dominance core, and network formation games," Games and Economic Behavior, Elsevier, vol. 66(1), pages 462-487, May.
    17. Laffond G. & Laslier, J. F. & Le Breton, M., 1996. "Condorcet choice correspondences: A set-theoretical comparison," Mathematical Social Sciences, Elsevier, vol. 31(1), pages 59-59, February.
    18. Felix Brandt & Maria Chudnovsky & Ilhee Kim & Gaku Liu & Sergey Norin & Alex Scott & Paul Seymour & Stephan Thomassé, 2013. "A counterexample to a conjecture of Schwartz," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 739-743, March.
    19. Han, Weibin & van Deemen, Adrian, 2021. "The solution of generalized stable sets and its refinement," Mathematical Social Sciences, Elsevier, vol. 113(C), pages 60-67.
    20. Hannu Vartiainen, 2015. "Dynamic stable set as a tournament solution," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 309-327, September.

    More about this item

    Keywords

    Choice function; rationalizable choice; stable set; vstability;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

    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:ris:qmetal:2015_005. 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: Julio Carmona (email available below). General contact details of provider: https://edirc.repec.org/data/dmalies.html .

    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.