IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v52y2019i2d10.1007_s00355-018-1146-0.html
   My bibliography  Save this article

Congruence relations on a choice space

Author

Listed:
  • Domenico Cantone

    (University of Catania)

  • Alfio Giarlotta

    (University of Catania)

  • Stephen Watson

    (York University)

Abstract

A choice space is a finite set of alternatives endowed with a map associating to each menu a nonempty subset of selected items. A congruence on a choice space is an equivalence relation that preserves its structure. Intuitively, two alternatives are congruent if the agent is indifferent between them, and, in addition, her choice is influenced by them in exactly the same way. We give an axiomatic characterization of the notion of congruence in terms of three natural conditions: binary fungibility, common destiny, and repetition irrelevance. Further, we show that any congruence satisfies the following desirable properties: (hereditariness) it induces a well-defined choice on the quotient set of equivalence classes; (reflectivity) the primitive behavior can be always retrieved from the quotient choice, regardless of any feature of rationality; (consistency) all basic axioms of choice consistency are preserved back and forth by passing to the quotient. We also prove that the family of all congruences on a choice space forms a lattice under set-inclusion, having equality as a minimum, and a unique maximum, called revealed indiscernibility. The latter relation can be seen as a limit form of revealed similarity as the agent’s rationality increases.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:52:y:2019:i:2:d:10.1007_s00355-018-1146-0
    DOI: 10.1007/s00355-018-1146-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00355-018-1146-0
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00355-018-1146-0?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. 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.
    2. Apesteguia, Jose & Ballester, Miguel A., 2013. "Choice by sequential procedures," Games and Economic Behavior, Elsevier, vol. 77(1), pages 90-99.
    3. 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.
    4. Paola Manzini & Marco Mariotti, 2007. "Sequentially Rationalizable Choice," American Economic Review, American Economic Association, vol. 97(5), pages 1824-1839, December.
    5. Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Y. Ozbay, 2012. "Revealed Attention," American Economic Review, American Economic Association, vol. 102(5), pages 2183-2205, August.
    6. Jamison, Dean T & Lau, Lawrence J, 1975. "Semiorders and the Theory of Choice: A Correction," Econometrica, Econometric Society, vol. 43(5-6), pages 979-980, Sept.-Nov.
    7. Chambers,Christopher P. & Echenique,Federico, 2016. "Revealed Preference Theory," Cambridge Books, Cambridge University Press, number 9781107087804.
    8. Herzberger, Hans G, 1973. "Ordinal Preference and Rational Choice," Econometrica, Econometric Society, vol. 41(2), pages 187-237, March.
    9. Schwartz, Thomas, 1976. "Choice functions, "rationality" conditions, and variations on the weak axiom of revealed preference," Journal of Economic Theory, Elsevier, vol. 13(3), pages 414-427, December.
    10. Gil Kalai & Ariel Rubinstein & Ran Spiegler, 2002. "Rationalizing Choice Functions By Multiple Rationales," Econometrica, Econometric Society, vol. 70(6), pages 2481-2488, November.
    11. Bandyopadhyay, Taradas & Sengupta, Kunal, 1993. "Characterization of Generalized Weak Orders and Revealed Preference," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(3), pages 571-576, July.
    12. Au, Pak Hung & Kawai, Keiichi, 2011. "Sequentially rationalizable choice with transitive rationales," Games and Economic Behavior, Elsevier, vol. 73(2), pages 608-614.
    13. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    14. Sen, Amartya, 1993. "Internal Consistency of Choice," Econometrica, Econometric Society, vol. 61(3), pages 495-521, May.
    15. 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.
    16. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Springer Books, Springer, edition 0, number 978-3-540-34183-3, September.
    17. Lleras, Juan Sebastián & Masatlioglu, Yusufcan & Nakajima, Daisuke & Ozbay, Erkut Y., 2017. "When more is less: Limited consideration," Journal of Economic Theory, Elsevier, vol. 170(C), pages 70-85.
    18. Kotaro Suzumura, 1976. "Rational Choice and Revealed Preference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 43(1), pages 149-158.
    19. Mandler, Michael, 2009. "Indifference and incompleteness distinguished by rational trade," Games and Economic Behavior, Elsevier, vol. 67(1), pages 300-314, September.
    20. Bandyopadhyay, Taradas & Sengupta, Kunal, 1991. "Revealed Preference Axioms for Rational Choice," Economic Journal, Royal Economic Society, vol. 101(405), pages 202-213, March.
    21. Giarlotta, Alfio & Greco, Salvatore, 2013. "Necessary and possible preference structures," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 163-172.
    22. Mauricio Ribeiro & Gil Riella, 2017. "Regular preorders and behavioral indifference," Theory and Decision, Springer, vol. 82(1), pages 1-12, January.
    23. Jamison, Dean T & Lau, Lawrence J, 1973. "Semiorders and the Theory of Choice," Econometrica, Econometric Society, vol. 41(5), pages 901-912, September.
    24. 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.
    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. Giarlotta, Alfio & Petralia, Angelo & Watson, Stephen, 2022. "Bounded rationality is rare," Journal of Economic Theory, Elsevier, vol. 204(C).
    2. Marta Cardin, 2023. "Rights Systems and Aggregation Functions on Property Spaces," Mathematics, MDPI, vol. 11(17), pages 1-10, August.
    3. Domenico Cantone & Alfio Giarlotta & Stephen Watson, 2021. "Choice resolutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 713-753, May.

    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. Domenico Cantone & Alfio Giarlotta & Stephen Watson, 2021. "Choice resolutions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(4), pages 713-753, May.
    2. Juan Lleras & Yusufcan Masatlioglu & Daisuke Nakajima & Erkut Ozbay, 2021. "Path-Independent Consideration," Games, MDPI, vol. 12(1), pages 1-10, March.
    3. García-Sanz, María D. & Alcantud, José Carlos R., 2015. "Sequential rationalization of multivalued choice," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 29-33.
    4. Tyson, Christopher J., 2008. "Cognitive constraints, contraction consistency, and the satisficing criterion," Journal of Economic Theory, Elsevier, vol. 138(1), pages 51-70, January.
    5. 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.
    6. Freeman, David J., 2017. "Preferred personal equilibrium and simple choices," Journal of Economic Behavior & Organization, Elsevier, vol. 143(C), pages 165-172.
    7. Alfio Giarlotta & Angelo Petralia & Stephen Watson, 2022. "Semantics meets attractiveness: Choice by salience," Papers 2204.08798, arXiv.org, revised Aug 2022.
    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. Gian Caspari & Manshu Khanna, 2021. "Non-Standard Choice in Matching Markets," Papers 2111.06815, arXiv.org.
    10. Georgios Gerasimou, 2016. "Partially dominant choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 127-145, January.
    11. Stewart, Rush T., 2020. "Weak pseudo-rationalizability," Mathematical Social Sciences, Elsevier, vol. 104(C), pages 23-28.
    12. 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.
    13. Jesper Armouti-Hansen & Christopher Kops, 2018. "This or that? Sequential rationalization of indecisive choice behavior," Theory and Decision, Springer, vol. 84(4), pages 507-524, June.
    14. Horan, Sean, 2016. "A simple model of two-stage choice," Journal of Economic Theory, Elsevier, vol. 162(C), pages 372-406.
    15. Christopher Tyson, 2015. "Satisficing behavior with a secondary criterion," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(3), pages 639-661, March.
    16. Valentino Dardanoni & Paola Manzini & Marco Mariotti & Christopher J. Tyson, 2020. "Inferring Cognitive Heterogeneity From Aggregate Choices," Econometrica, Econometric Society, vol. 88(3), pages 1269-1296, May.
    17. Yuta Inoue & Koji Shirai, 2018. "Limited consideration and limited data: revealed preference tests and observable restrictions," Discussion Paper Series 176, School of Economics, Kwansei Gakuin University, revised Mar 2018.
    18. Paola Manzini & Marco Mariotti, 2015. "State dependent choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 45(2), pages 239-268, September.
    19. Tyson, Christopher J., 2008. "Cognitive constraints, contraction consistency, and the satisficing criterion," Journal of Economic Theory, Elsevier, vol. 138(1), pages 51-70, January.

    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:52:y:2019:i:2:d:10.1007_s00355-018-1146-0. 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.