Representing preferences with nontransitive indifference by a single real-valued function
A preference relation on a set \(X\) is a binary asymmetric relation. Interval orders are a class of preference relations. In this paper, the authors consider three classes of interval orders which are complete preorders. They give sufficient conditions for the existence of continuous utility functions representing these complete preorders when \(X\) is a topological space. For this, they use the notion of strong separability introduced by \textit{A. Chateauneuf} [J. Math. Econ. 16, 139-146 (1987; Zbl 0642.90017)]. They also consider the existence of continuous functions representing a strongly separable interval order when \(X\) is a measurable topological space. \{Reviewer's remark: The classes of interval orders introduced by the authors can probably be related to the covering relation and the Gillies relation which are used in the political games literature\}.
existence of continuous utility functions
scientific article; zbMATH DE number 842074