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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.

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
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. 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.
    2. 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.
    3. Eric Danan, 2010. "Randomization vs. Selection: How to Choose in the Absence of Preference?," Management Science, INFORMS, vol. 56(3), pages 503-518, March.
    4. Hill, Brian, 2011. "Deferral, incomplete preferences and confidence," Les Cahiers de Recherche 940, HEC Paris.
    5. Mc Kiernan, Daniel Kian, 2012. "Indifference, indecision, and coin-flipping," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 237-246.
    6. 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.
    7. Gerasímou, Georgios, 2010. "Consumer theory with bounded rational preferences," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 708-714, September.
    8. 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.
    9. Mandler, Michael, 2015. "Rational agents are the quickest," Journal of Economic Theory, Elsevier, vol. 155(C), pages 206-233.
    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. Gerasimou, Georgios, 2010. "Rational indecisive choice," MPRA Paper 25481, University Library of Munich, Germany.
    12. 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).
    13. Gerasimou, Georgios, 2015. "Indecisiveness, Undesirability and Overload Revealed Through Rational Choice Deferral," MPRA Paper 67290, University Library of Munich, Germany.

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