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Continuity, completeness and the definition of weak preferences

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  • Karni, Edi

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.

Suggested Citation

  • Karni, Edi, 2011. "Continuity, completeness and the definition of weak preferences," Mathematical Social Sciences, Elsevier, vol. 62(2), pages 123-125, September.
    • Handle: RePEc:eee:matsoc:v:62:y:2011:i:2:p:123-125
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Schmeidler, David, 1971. "A Condition for the Completeness of Partial Preference Relations," Econometrica, Econometric Society, vol. 39(2), pages 403-404, March.
    4. Dubra, Juan, 2011. "Continuity and completeness under risk," Mathematical Social Sciences, Elsevier, vol. 61(1), pages 80-81, January.
    5. Juan Dubra & Fabio Maccheroni & Efe A. Ok, 2004. "Expected Utility Without the Completeness Axiom," Yale School of Management Working Papers ysm404, Yale School of Management.
    6. 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.
    7. Tsogbadral Galaabaatar & Edi Karni, 2013. "Subjective Expected Utility With Incomplete Preferences," Econometrica, Econometric Society, vol. 81(1), pages 255-284, January.
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    Cited by:

    1. Karni, Edi & Vierø, Marie-Louise, 2023. "Comparative incompleteness: Measurement, behavioral manifestations and elicitation," Journal of Economic Behavior & Organization, Elsevier, vol. 205(C), pages 423-442.
    2. Galaabaatar, Tsogbadral & Karni, Edi, 2012. "Expected multi-utility representations," Mathematical Social Sciences, Elsevier, vol. 64(3), pages 242-246.
    3. Robert G. Chambers & Tigran Melkonyan & John Quiggin, 2022. "Incomplete preferences, willingness to pay, and willingness to accept," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(3), pages 727-761, October.
    4. McCarthy, David & Mikkola, Kalle, 2018. "Continuity and completeness of strongly independent preorders," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 141-145.
    5. Edi Karni, 2014. "Familiarity breeds completeness," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 109-124, May.
    6. Chambers, Robert G., 2014. "Uncertain equilibria and incomplete preferences," Journal of Mathematical Economics, Elsevier, vol. 55(C), pages 48-54.
    7. Karni, Edi & Safra, Zvi, 2015. "Continuity, completeness, betweenness and cone-monotonicity," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 68-72.
    8. Diecidue, Enrico & Somasundaram, Jeeva, 2017. "Regret theory: A new foundation," Journal of Economic Theory, Elsevier, vol. 172(C), pages 88-119.
    9. 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.

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