This paper explores the concept of a social evaluation functional in the case of an arbitrary set of alternatives. In the first part, a characterization of projective social evaluations functionals is shown whenever the common restricted domain is the set of all bounded utility functions equipped with the supremum norm topology. The result makes a crucial use, among others, of a continuity axiom. In the second part, a comparison meaningful property is introduced for a social evaluation functional which allows us for obtaining a more general result with no continuity requirements. Finally, an impossibility theorem, which is reminiscent of that is obtained by Chichilnisky in (Q J Econ 97:337–352, 1982) but without using topological conditions, is offered.

本文探讨了在任意一组备选方案的情况下社会评价函数的概念。在第一部分中，只要公共限制域是配备有最高范数拓扑的所有有界效用函数的集合，就会显示投射社会评价泛函的特征。该结果对连续性公理等起到了关键作用。在第二部分中，为社会评价函数引入了比较有意义的属性，这使我们能够在没有连续性要求的情况下获得更一般的结果。最后，提供了一个不可能性定理，它让人想起 Chichilnisky 在 (QJ Econ 97:337–352, 1982) 中获得的那个，但没有使用拓扑条件。