Utility Functions and Constrained Additivity

摘要

In this paper, we study utility functions acting on score vectors from [0,1]^{n, and, in particular, we consider normed utility functions, which are also known as aggregation functions. We focus our study on the constrained additivity of the considered functions, i.e., on their additivity on special subdomains. Several well-known properties, such as homogeneity, unanimity, self-duality, shift-invariantness, etc., are shown to be particular instances of constrained additivity. Moreover, some non-trivial constrained additive utility functions are presented. We also open a problem concerning the existence of a minimal relation characterizing a considered constrained additivity and the standard additivity as well.}