IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v66y2018i1d10.1007_s00199-017-1057-9.html
   My bibliography  Save this article

The structure of incomplete preferences

Author

Listed:
  • Leandro Gorno

    (FGV/EPGE - Escola Brasileira de Economia e Finanças)

Abstract

I study incomplete preferences as a means to represent indecisiveness. A decomposition into maximal domains of comparability is characterized and used to link optimization of incomplete preferences with maximization of local utility functions. Larger maximal domains are shown to correspond to more decisive preferences. The decomposition can be uniquely recovered from choice data under standard assumptions. Applications to different models within decision theory are discussed.

Suggested Citation

  • Leandro Gorno, 2018. "The structure of incomplete preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(1), pages 159-185, July.
    • Handle: RePEc:spr:joecth:v:66:y:2018:i:1:d:10.1007_s00199-017-1057-9
    DOI: 10.1007/s00199-017-1057-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-017-1057-9
    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/s00199-017-1057-9?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. Özgür Evren, 2012. "Scalarization Methods and Expected Multi-Utility Representations," Working Papers w0174, New Economic School (NES).
    2. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
    3. Mauricio Ribeiro & Gil Riella, 2017. "Regular preorders and behavioral indifference," Theory and Decision, Springer, vol. 82(1), pages 1-12, January.
    4. Walker, Mark, 1979. "A Generalization of the Maximum Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(1), pages 267-272, February.
    5. Karni, Edi & Safra, Zvi, 2015. "Continuity, completeness, betweenness and cone-monotonicity," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 68-72.
    6. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
    7. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    8. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
    9. Dubra, Juan, 2011. "Continuity and completeness under risk," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 80-81, January.
    10. Gil Riella, 2015. "On the representation of incomplete preferences under uncertainty with indecisiveness in tastes and beliefs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(3), pages 571-600, April.
    11. Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
    12. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    13. Efe A. Ok & Pietro Ortoleva & Gil Riella, 2012. "Incomplete Preferences Under Uncertainty: Indecisiveness in Beliefs versus Tastes," Econometrica, Econometric Society, vol. 80(4), pages 1791-1808, July.
    14. Peleg, Bezalel, 1970. "Utility Functions for Partially Ordered Topological Spaces," Econometrica, Econometric Society, vol. 38(1), pages 93-96, January.
    15. Rader, Trout, 1972. "Theory of Microeconomics," Elsevier Monographs, Elsevier, edition 1, number 9780125750509.
    16. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, vol. 56(1), pages 61-86, July.
    17. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, October.
    18. Evren, Özgür & Ok, Efe A., 2011. "On the multi-utility representation of preference relations," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 554-563.
    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. Furtado, Bruno A. & Nascimento, Leandro & Riella, Gil, 2023. "Rational choice with full-comparability domains," Journal of Economic Behavior & Organization, Elsevier, vol. 216(C), pages 124-135.
    2. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    3. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    4. Leandro Gorno & Alessandro Rivello, 2020. "Connected Incomplete Preferences," Papers 2008.04401, arXiv.org.

    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. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    2. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2021. "Expected utility theory on mixture spaces without the completeness axiom," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    3. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2017. "Representation of strongly independent preorders by sets of scalar-valued functions," MPRA Paper 79284, University Library of Munich, Germany.
    4. M. Ali Khan & Metin Uyanık, 2021. "Topological connectedness and behavioral assumptions on preferences: a two-way relationship," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 411-460, March.
    5. Özgür Evren, 2012. "Scalarization Methods and Expected Multi-Utility Representations," Working Papers w0174, Center for Economic and Financial Research (CEFIR).
    6. Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
    7. Giarlotta, Alfio & Greco, Salvatore, 2013. "Necessary and possible preference structures," Journal of Mathematical Economics, Elsevier, vol. 49(2), pages 163-172.
    8. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
    9. Leandro Nascimento, 2011. "Remarks on the consumer problem under incomplete preferences," Theory and Decision, Springer, vol. 70(1), pages 95-110, January.
    10. Eric Danan, 2010. "Randomization vs. Selection: How to Choose in the Absence of Preference?," Management Science, INFORMS, vol. 56(3), pages 503-518, March.
    11. Cosimo Munari, 2021. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Finance and Stochastics, Springer, vol. 25(1), pages 77-99, January.
    12. Weixuan Xia, 2023. "Optimal Consumption--Investment Problems under Time-Varying Incomplete Preferences," Papers 2312.00266, arXiv.org, revised Jan 2025.
    13. Galaabaatar, Tsogbadral & Khan, M. Ali & Uyanık, Metin, 2019. "Completeness and transitivity of preferences on mixture sets," Mathematical Social Sciences, Elsevier, vol. 99(C), pages 49-62.
    14. McCarthy, David & Mikkola, Kalle & Thomas, Teruji, 2020. "Utilitarianism with and without expected utility," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 77-113.
    15. Simone Cerreia-Vioglio & Alfio Giarlotta & Salvatore Greco & Fabio Maccheroni & Massimo Marinacci, 2020. "Rational preference and rationalizable choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 61-105, February.
    16. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    17. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    18. Minardi, Stefania & Savochkin, Andrei, 2015. "Preferences with grades of indecisiveness," Journal of Economic Theory, Elsevier, vol. 155(C), pages 300-331.
    19. Simone Cerreia-Vioglio & Alfio Giarlotta & Salvatore Greco & Fabio Maccheroni & Massimo Marinacci, 2020. "Rational preference and rationalizable choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 61-105, February.
    20. Itzhak Gilboa & Fabio Maccheroni & Massimo Marinacci & David Schmeidler, 2010. "Objective and Subjective Rationality in a Multiple Prior Model," Econometrica, Econometric Society, vol. 78(2), pages 755-770, March.

    More about this item

    Keywords

    Incomplete preferences; Indecisiveness; Maximal elements; Best elements; Revealed preference;
    All these keywords.

    JEL classification:

    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    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:joecth:v:66:y:2018:i:1:d:10.1007_s00199-017-1057-9. 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.