Svoboda | Graniru | BBC Russia | Golosameriki | Facebook
IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v112y2024ics0304406824000454.html
   My bibliography  Save this article

Smallest quasi-transitive extensions

Author

Listed:
  • Bossert, Walter
  • Cato, Susumu
  • Kamaga, Kohei

Abstract

Quasi-transitivity is a weakening of transitivity that has some attractive features, such as the important role it plays in the context of path-independent choice. However, the property suffers from the shortcoming that it does not allow for the existence of a closure operator. This paper examines the question to what extent an alternative operator can be defined that may then be used to ameliorate some of the limitations of quasi-transitivity imposed by the absence of a well-defined closure. To do so, we define the concept of a smallest quasi-transitive extension. A novel weakening of quasi-transitivity turns out to be necessary and sufficient for the existence of such a smallest extension. As an illustration, we apply the notion of a smallest quasi-transitive extension in the context of rational choice on arbitrary domains.

Suggested Citation

  • Bossert, Walter & Cato, Susumu & Kamaga, Kohei, 2024. "Smallest quasi-transitive extensions," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    • Handle: RePEc:eee:mateco:v:112:y:2024:i:c:s0304406824000454
    DOI: 10.1016/j.jmateco.2024.102983
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406824000454
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2024.102983?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. Suzumura, Kotaro, 1999. "Paretian Welfare Judgements and Bergsonian Social Choice," Economic Journal, Royal Economic Society, vol. 109(455), pages 204-220, April.
    2. Blair, Douglas H. & Bordes, Georges & Kelly, Jerry S. & Suzumura, Kotaro, 1976. "Impossibility theorems without collective rationality," Journal of Economic Theory, Elsevier, vol. 13(3), pages 361-379, December.
    3. Susumu Cato, 2016. "Rationality and Operators," SpringerBriefs in Economics, Springer, number 978-981-10-1896-1, October.
    4. Amartya Sen, 1969. "Quasi-Transitivity, Rational Choice and Collective Decisions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 381-393.
    5. Bossert, Walter & Suzumura, Kotaro, 2010. "Consistency, Choice, and Rationality," Economics Books, Harvard University Press, number 9780674052994, Spring.
    6. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    7. repec:bla:econom:v:72:y:2005:i:286:p:185-200 is not listed on IDEAS
    8. Suzumura, Kotaro, 1977. "Houthakker's axiom in the theory of rational choice," Journal of Economic Theory, Elsevier, vol. 14(2), pages 284-290, April.
    9. Kotaro Suzumura, 1976. "Rational Choice and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(1), pages 149-158.
    10. Susumu Cato, 2012. "Szpilrajn, Arrow And Suzumura: Concise Proofs Of Extension Theorems And An Extension," Metroeconomica, Wiley Blackwell, vol. 63(2), pages 235-249, May.
    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. Georges Bordes, 1976. "Consistency, Rationality and Collective Choice," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(3), pages 451-457.
    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. Walter Bossert & Marc Fleurbaey, 2015. "An Interview with Kotaro Suzumura," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(1), pages 179-208, January.
    2. Clark, Stephen A., 1995. "Indecisive choice theory," Mathematical Social Sciences, Elsevier, vol. 30(2), pages 155-170, October.
    3. Susumu Cato, 2018. "Choice functions and weak Nash axioms," Review of Economic Design, Springer;Society for Economic Design, vol. 22(3), pages 159-176, December.
    4. 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.
    5. 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.
    6. Bandyopadhyay, Taradas & Sengupta, Kunal, 2003. "Intransitive indifference and rationalizability of choice functions on general domains," Mathematical Social Sciences, Elsevier, vol. 46(3), pages 311-326, December.
    7. Taradas Bandyopadhyay, 2011. "Choice procedures and power structure in social decisions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(4), pages 597-608, October.
    8. Susumu Cato, 2018. "Collective rationality and decisiveness coherence," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 50(2), pages 305-328, February.
    9. 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.
    10. Santosh C. Panda, 2018. "Rational Choice with Intransitive Preferences," Studies in Microeconomics, , vol. 6(1-2), pages 66-83, June.
    11. Brandt, Felix & Harrenstein, Paul, 2011. "Set-rationalizable choice and self-stability," Journal of Economic Theory, Elsevier, vol. 146(4), pages 1721-1731, July.
    12. Kotaro Suzumura, 2020. "Reflections on Arrow’s research program of social choice theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(2), pages 219-235, March.
    13. Walter Bossert & Kotaro Suzumura, 2012. "Revealed preference and choice under uncertainty," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 247-258, March.
    14. Taposik Banerjee, 2024. "Characterization of a k-th best element rationalizable choice function with full domain," Theory and Decision, Springer, vol. 96(4), pages 503-516, June.
    15. Walter Bossert & Yves Sprumont & Kotaro Suzumura, 2006. "Rationalizability of choice functions on general domains without full transitivity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(3), pages 435-458, December.
    16. Susumu Cato, 2013. "Quasi-decisiveness, quasi-ultrafilter, and social quasi-orderings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 169-202, June.
    17. Conal Duddy & Ashley Piggins, 2018. "On some oligarchy results when social preference is fuzzy," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(4), pages 717-735, December.
    18. Bossert, Walter & Suzumura, Kotaro, 2007. "Social Norms and Rationality of Choice," Cahiers de recherche 2007-07, Universite de Montreal, Departement de sciences economiques.
    19. Walter Bossert & Kotaro Suzumura, 2012. "Quasi-transitive and Suzumura consistent relations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 323-334, July.
    20. John Duggan, 2019. "Weak rationalizability and Arrovian impossibility theorems for responsive social choice," Public Choice, Springer, vol. 179(1), pages 7-40, April.

    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:112:y:2024:i:c:s0304406824000454. 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.