# Continuity and completeness under risk

*Juan Dubra* ()

*Mathematical Social Sciences*, 2011, vol. 61, issue 1, 80-81

**Abstract:**
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.

**Keywords:** Incomplete; preferences; Independence; axiom; Archimedean; property (search for similar items in EconPapers)

**Date:** 2011

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**Related works:**

Working Paper: Continuity and Completeness under Risk (2010)

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:matsoc:v:61:y:2011:i:1:p:80-81

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