Comparison meaningful operators and ordinal invariant preferences

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:432

Article

Candeal, Juan C.¹  Indurain, Esteban² 

[1] Univ Zaragoza, Dept Anal Econ, Fac Econ & Empresa, Zaragoza 50005, Spain

[2] Univ Publ Navarra, Dept Matemat, Navarra, Spain

关键词: Comparison meaningfulness;    Ordinal invariant preferences;    Ordinal covariant operators;    Measurement theory;    Social choice theory;   

DOI  :  10.1016/j.jmaa.2015.07.017

来源: Elsevier

【 摘 要 】

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 Omega, 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 Omega, 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free