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Continuity, completeness and the definition of weak preferences

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  • Karni, Edi
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    Abstract

    This note explores the connections between continuity and completeness under alternative conceptions of preference relations. For non-trivial preorders, it shows that, unlike the standard definitions, the weak preference relation defined in Galaabaatar and Karni (2010) allows for incomplete preferences while maintaining all the continuity properties of complete preference relations. It also makes it possible to distinguish indifference between alternatives from non-comparability of alternatives. If the preference relations are complete, this definition agrees with the customary definitions.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0165489611000436
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    Bibliographic Info

    Article provided by Elsevier in its journal Mathematical Social Sciences.

    Volume (Year): 62 (2011)
    Issue (Month): 2 (September)
    Pages: 123-125

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    Handle: RePEc:eee:matsoc:v:62:y:2011:i:2:p:123-125

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    Web page: http://www.elsevier.com/locate/inca/505565

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    1. 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.
    2. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-04, March.
    3. Chateauneuf, Alain, 1987. "Continuous representation of a preference relation on a connected topological space," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 139-146, April.
    4. Dubra, Juan, 2011. "Continuity and completeness under risk," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 80-81, January.
    5. Tsogbadral Galaabaatar & Edi Karni, 2010. "Objective and Subjective Expected Utility with Incomplete Preferences," Economics Working Paper Archive 572, The Johns Hopkins University,Department of Economics.
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    Cited by:
    1. Galaabaatar, Tsogbadral & Karni, Edi, 2012. "Expected multi-utility representations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 242-246.

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