Continuity and completeness of strongly independent preorders

TY - JOUR

T1 - Continuity and completeness of strongly independent preorders

AU - McCarthy, David

AU - Mikkola, Kalle

PY - 2018/5

Y1 - 2018/5

N2 - We show that a strongly independent preorder on a possibly infinite dimensional convex set that satisfies 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 satisfies 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, illustrating the relevance of infinite dimensionality. (C) 2018 Elsevier B.V. All rights reserved.

AB - We show that a strongly independent preorder on a possibly infinite dimensional convex set that satisfies 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 satisfies 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, illustrating the relevance of infinite dimensionality. (C) 2018 Elsevier B.V. All rights reserved.

KW - MULTI-UTILITY REPRESENTATIONS

KW - INCOMPLETE PREFERENCES

KW - EXPECTED UTILITY

U2 - 10.1016/j.mathsocsci.2018.03.004

DO - 10.1016/j.mathsocsci.2018.03.004

M3 - Article

VL - 93

SP - 141

EP - 145

JO - MATHEMATICAL SOCIAL SCIENCES

T2 - MATHEMATICAL SOCIAL SCIENCES

JF - MATHEMATICAL SOCIAL SCIENCES

SN - 0165-4896

ER -