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Indifference and incompleteness distinguished by rational trade

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  • 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.

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  • 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
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    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.
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    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.

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