Comparison meaningful operators and ordinal invariant preferences
Fecha
2015Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Identificador del proyecto
Impacto
|
10.1016/j.jmaa.2015.07.017
Resumen
The existence of a continuous and order-preserving real-valued function, for the class of continuous and ordinal invariant total preorders, defined on the Banach space of all bounded real-valued functions, which are in turn defined on a given set Ω, is characterized. Whenever the total preorder is nontrivial, the type of representation obtained leads to a functional equation that is closely relat ...
[++]
The existence of a continuous and order-preserving real-valued function, for the class of continuous and ordinal invariant total preorders, defined on the Banach space of all bounded real-valued functions, which are in turn defined on a given set Ω, is characterized. Whenever the total preorder is nontrivial, the type of representation obtained leads to a functional equation that is closely related to the concept of comparison meaningfulness, and is studied in detail in this setting. In particular, when restricted to the space of bounded and measurable real-valued functions, with respect to some algebra of subsets of Ω, we prove that, if the total preorder is also weakly Paretian, then it can be represented as a Choquet integral with respect to a {0,1}-valued capacity. Some interdisciplinary applications to measurement theory and social choice are also considered. [--]
Materias
Comparison meaningfulness,
Ordinal invariant preferences,
Ordinal covariant operators,
Measurement theory,
Social choice theory
Editor
Elsevier
Publicado en
Journal of Mathematical Analysis and Applications (2015)
Departamento
Universidad Pública de Navarra. Departamento de Matemáticas /
Nafarroako Unibertsitate Publikoa. Matematika Saila
Versión del editor
Entidades Financiadoras
This work has been partially supported by the research projects ECO2012-34828, MTM2012-37894-C02-02 and TIN2013-40765-P (Spain).