Continuity and completeness of strongly independent preorders

Mathematical Social Sciences 93:141-145 (2018)
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Abstract

A strongly independent preorder on a possibly in finite dimensional convex set that satisfi es two of the following conditions must satisfy the third: (i) the Archimedean continuity condition; (ii) mixture continuity; and (iii) comparability under the preorder is an equivalence relation. In addition, if the preorder is nontrivial (has nonempty asymmetric part) and satisfi es two of the following conditions, it must satisfy the third: (i') a modest strengthening of the Archimedean condition; (ii') mixture continuity; and (iii') completeness. Applications to decision making under conditions of risk and uncertainty are provided.

Author Profiles

Kalle M. Mikkola
Aalto University
David McCarthy
University of Hong Kong

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