Continuity, completeness and the definition of weak preferences
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 inÂ 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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References listed on IDEAS
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- 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.
- Juan Dubra & Fabio Maccheroni & Efe Oki, 2001.
"Expected utility theory without the completeness axiom,"
ICER Working Papers - Applied Mathematics Series
11-2001, ICER - International Centre for Economic Research.
- 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.
- Juan Dubra & Fabio Maacheroni & Efe A. Ok, 2001. "Expected Utility Theory without the Completeness Axiom," Cowles Foundation Discussion Papers 1294, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Schmeidler, David, 1971.
"A Condition for the Completeness of Partial Preference Relations,"
Econometric Society, vol. 39(2), pages 403-404, March.
- SCHMEIDLER, David, "undated". "A condition for the completeness of partial preference relations," CORE Discussion Papers RP 86, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Dubra, Juan, 2011.
"Continuity and completeness under risk,"
Mathematical Social Sciences,
Elsevier, vol. 61(1), pages 80-81, January.
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