IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v67y2009i1p300-314.html
   My bibliography  Save this article

Indifference and incompleteness distinguished by rational trade

Author

Listed:
  • Mandler, Michael

Abstract

We use an agent's strict preferences to define indifference and incompleteness relations that identify the sequences of trades that are rational to undertake. If an agent makes sequences of trades of options labeled indifferent, the agent will never be led to an inferior outcome, but trades of options where no preference judgments obtain can lead to diminished welfare. For one-shot choices, in contrast, there can be no behavioral distinction between indifference and incompleteness. Applications include: an isomorphism for incomplete preferences that indicates when weak and strict preferences contain interchangeable information, a characterization of the (possibly incomplete) preference relations consistent with a one-shot choice function, and an equivalent definition of incompleteness that relies on the philosophical theory of incommensurability.

Suggested Citation

  • Mandler, Michael, 2009. "Indifference and incompleteness distinguished by rational trade," Games and Economic Behavior, Elsevier, vol. 67(1), pages 300-314, September.
    • Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:300-314
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(08)00213-3
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. 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.
    2. Masatlioglu, Yusufcan & Ok, Efe A., 2005. "Rational choice with status quo bias," Journal of Economic Theory, Elsevier, vol. 121(1), pages 1-29, March.
    3. 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.
    4. Paola Manzini & Marco Mariotti, 2008. "On the Representation of Incomplete Preferences Over Risky Alternatives," Theory and Decision, Springer, vol. 65(4), pages 303-323, December.
    5. Michael Mandler, 2004. "Status quo maintenance reconsidered: changing or incomplete preferences?," Economic Journal, Royal Economic Society, vol. 114(499), pages 518-535, November.
    6. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, vol. 50(2), pages 255-277, February.
    7. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, vol. 104(2), pages 429-449, June.
    8. 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.
    9. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-1091, November.
    10. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers 807, Cowles Foundation for Research in Economics, Yale University.
    11. 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.
    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. Harvey Lederman, 2023. "Incompleteness, Independence, and Negative Dominance," Papers 2311.08471, arXiv.org.
    2. Brian Hill, 2012. "Confidence in preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 273-302, July.
    3. Georgios Gerasimou, 2018. "Indecisiveness, Undesirability and Overload Revealed Through Rational Choice Deferral," Economic Journal, Royal Economic Society, vol. 128(614), pages 2450-2479, September.
    4. Manzini, Paola & Mariotti, Marco & Tyson, Christopher J., 2016. "Partial knowledge restrictions on the two-stage threshold model of choice," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 41-47.
    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. Mandler, Michael, 2015. "Rational agents are the quickest," Journal of Economic Theory, Elsevier, vol. 155(C), pages 206-233.
    7. Gerasimou, Georgios, 2010. "Rational indecisive choice," MPRA Paper 25481, University Library of Munich, Germany.
    8. Eric Danan, 2010. "Randomization vs. Selection: How to Choose in the Absence of Preference?," Management Science, INFORMS, vol. 56(3), pages 503-518, March.
    9. Cato, Susumu, 2018. "Incomplete decision-making and Arrow’s impossibility theorem," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 58-64.
    10. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    11. Brian Hill, 2011. "Deferral, incomplete preferences and confidence," Working Papers hal-00625420, HAL.
    12. Georgios Gerasimou, 2021. "Towards Eliciting Weak or Incomplete Preferences in the Lab: A Model-Rich Approach," Papers 2111.14431, arXiv.org, revised Dec 2023.
    13. 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.
    14. Manzini, Paola & Mariotti, Marco & Tyson, Christopher J, 2015. "Partial Knowledge Restrictions on theTwo-Stage Threshold Model of Choice," 2007 Annual Meeting, July 29-August 1, 2007, Portland, Oregon TN 2015-58, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    15. Manzini, Paola & Mariotti, Marco & Tyson, Christopher J., 2016. "Partial knowledge restrictions on the two-stage threshold model of choice," Journal of Mathematical Economics, Elsevier, vol. 64(C), pages 41-47.
    16. Mc Kiernan, Daniel Kian, 2012. "Indifference, indecision, and coin-flipping," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 237-246.
    17. Gerasimou, Georgios, 2012. "Asymmetric Dominance, Deferral and Status Quo Bias in a Theory of Choice with Incomplete Preferences," MPRA Paper 40097, University Library of Munich, Germany.
    18. Michael Mandler, 2021. "The lexicographic method in preference theory," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(2), pages 553-577, March.
    19. Georgios Gerasimou, 2016. "Partially dominant choice," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 61(1), pages 127-145, January.
    20. 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.

    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. Eric Danan, 2010. "Randomization vs. Selection: How to Choose in the Absence of Preference?," Management Science, INFORMS, vol. 56(3), pages 503-518, March.
    2. Cettolin, E. & Riedl, A.M., 2015. "Revealed incomplete preferences under uncertainty," Research Memorandum 016, Maastricht University, Graduate School of Business and Economics (GSBE).
    3. Evren, Özgür, 2014. "Scalarization methods and expected multi-utility representations," Journal of Economic Theory, Elsevier, vol. 151(C), pages 30-63.
    4. Cettolin, Elena & Riedl, Arno, 2019. "Revealed preferences under uncertainty: Incomplete preferences and preferences for randomization," Journal of Economic Theory, Elsevier, vol. 181(C), pages 547-585.
    5. Kraus, Alan & Sagi, Jacob S., 2006. "Inter-temporal preference for flexibility and risky choice," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 698-709, September.
    6. Bosi, Gianni & Herden, Gerhard, 2012. "Continuous multi-utility representations of preorders," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 212-218.
    7. Qiyan Ong & Jianying Qiu, 2023. "Paying for randomization and indecisiveness," Journal of Risk and Uncertainty, Springer, vol. 67(1), pages 45-72, August.
    8. Özgür Evren, 2012. "Scalarization Methods and Expected Multi-Utility Representations," Working Papers w0174, New Economic School (NES).
    9. Harvey Lederman, 2023. "Incompleteness, Independence, and Negative Dominance," Papers 2311.08471, arXiv.org.
    10. Leandro Nascimento, 2011. "Remarks on the consumer problem under incomplete preferences," Theory and Decision, Springer, vol. 70(1), pages 95-110, January.
    11. 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).
    12. Wesley H. Holliday & Mikayla Kelley, 2021. "Escaping Arrow's Theorem: The Advantage-Standard Model," Papers 2108.01134, arXiv.org, revised Nov 2022.
    13. van Hees, Martin & Jitendranath, Akshath & Luttens, Roland Iwan, 2021. "Choice functions and hard choices," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    14. 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.
    15. 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.
    16. Jose Apesteguia & Miguel Ballester, 2009. "A theory of reference-dependent behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 427-455, September.
    17. Cosimo Munari, 2020. "Multi-utility representations of incomplete preferences induced by set-valued risk measures," Papers 2009.04151, arXiv.org.
    18. Gerasimou, Georgios, 2010. "Rational indecisive choice," MPRA Paper 25481, University Library of Munich, Germany.
    19. John Duggan, 2019. "Weak rationalizability and Arrovian impossibility theorems for responsive social choice," Public Choice, Springer, vol. 179(1), pages 7-40, April.
    20. Gorno, Leandro & Rivello, Alessandro T., 2023. "A maximum theorem for incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 106(C).

    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:gamebe:v:67:y:2009:i:1:p:300-314. 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/inca/622836 .

    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.