Point-Sensitive Aggregation Operators: Functional Equations and Applications to Social Choice

Abstract

In this paper we study aggregation operators that are point-sensitive which means that their values depend on the point where the functions to be aggregated are defined, as well as on the values of those functions at that point. This analysis gives rise to consider several functional equations that appear in a natural way. Further applications in mathematical social choice also appear as a by-product. In particular, we characterize the representation of certain social choice rules by means of specific numerical functions.