Continuity and Completeness under Risk
Suppose some non-degenerate preferences R, with strict part P, over risky outcomes satisfy Independence. Then, when they satisfy any two of the following axioms, they satisfy the third. Herstein-Milnor: for all lotteries p,q,r, the set of a's for which ap+(1-a)qRr is closed. Archimedean: for all p,q,r there exists a>0 such that if pPq, then ap+(1-a)rPq. Complete: for all p,q, either pRq or qRp.
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- Schmeidler, David, 1971.
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Econometric Society, vol. 39(2), pages 403-04, March.
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- Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004.
"Expected utility theory without the completeness axiom,"
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- 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.
- Karni, Edi, 2007. "Archimedean and continuity," Mathematical Social Sciences, Elsevier, vol. 53(3), pages 332-334, May.
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