Continuity and completeness of strongly independent preorders
Tutkimustuotos: Lehtiartikkeli › › vertaisarvioitu
Standard
Continuity and completeness of strongly independent preorders. / McCarthy, David; Mikkola, Kalle.
julkaisussa: MATHEMATICAL SOCIAL SCIENCES, Vuosikerta 93, 05.2018, s. 141-145.Tutkimustuotos: Lehtiartikkeli › › vertaisarvioitu
Harvard
APA
Vancouver
Author
Bibtex - Lataa
}
RIS - Lataa
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 -
ID: 27672036