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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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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 67 (2009)
Issue (Month): 1 (September)
Pages: 300-314

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Handle: RePEc:eee:gamebe:v:67:y:2009:i:1:p:300-314

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Web page: http://www.elsevier.com/locate/inca/622836

Related research

Keywords: Incomplete preferences Indifference Sequential rationality Revealed preference Incommensurability;

References

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  1. Ok, Efe A., 2002. "Utility Representation of an Incomplete Preference Relation," Journal of Economic Theory, Elsevier, Elsevier, vol. 104(2), pages 429-449, June.
  2. Michael Mandler, 2004. "Status quo maintenance reconsidered: changing or incomplete preferences?," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 114(499), pages F518-F535, November.
  3. Paola Manzini & Marco Mariotti, 2008. "On the Representation of Incomplete Preferences Over Risky Alternatives," Theory and Decision, Springer, Springer, vol. 65(4), pages 303-323, December.
  4. Masatlioglu, Yusufcan & Ok, Efe A., 2005. "Rational choice with status quo bias," Journal of Economic Theory, Elsevier, Elsevier, vol. 121(1), pages 1-29, March.
  5. Schwartz, Thomas, 1976. "Choice functions, "rationality" conditions, and variations on the weak axiom of revealed preference," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(3), pages 414-427, December.
  6. Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, Econometric Society, vol. 41(6), pages 1075-91, November.
  7. Blair, Douglas H. & Bordes, Georges & Kelly, Jerry S. & Suzumura, Kotaro, 1976. "Impossibility theorems without collective rationality," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(3), pages 361-379, December.
  8. Eliaz, Kfir & Ok, Efe A., 2006. "Indifference or indecisiveness? Choice-theoretic foundations of incomplete preferences," Games and Economic Behavior, Elsevier, Elsevier, vol. 56(1), pages 61-86, July.
  9. Mandler, Michael, 2005. "Incomplete preferences and rational intransitivity of choice," Games and Economic Behavior, Elsevier, Elsevier, vol. 50(2), pages 255-277, February.
  10. Bandyopadhyay, Taradas & Sengupta, Kunal, 1993. "Characterization of Generalized Weak Orders and Revealed Preference," Economic Theory, Springer, Springer, vol. 3(3), pages 571-76, July.
  11. Truman F. Bewley, 1986. "Knightian Decision Theory: Part 1," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 807, Cowles Foundation for Research in Economics, Yale University.
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Cited by:
  1. 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.
  2. Gerasimou, Georgios, 2010. "Rational indecisive choice," MPRA Paper 25481, University Library of Munich, Germany.
  3. Gerasimou, Georgios, 2009. "Consumer theory with bounded rational preferences," MPRA Paper 18673, University Library of Munich, Germany, revised 16 Nov 2009.
  4. Mc Kiernan, Daniel Kian, 2012. "Indifference, indecision, and coin-flipping," Journal of Mathematical Economics, Elsevier, vol. 48(4), pages 237-246.
  5. Brian Hill, 2012. "Confidence in preferences," Social Choice and Welfare, Springer, Springer, vol. 39(2), pages 273-302, July.
  6. Hill, Brian, 2011. "Deferral, incomplete preferences and confidence," Les Cahiers de Recherche 940, HEC Paris.

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