From a formal point of view, a composite indicator is an aggregate of all dimensions, objectives, individual indicators and variables used for its construction. This implies that what defines a composite indicator is the set of properties underlying its mathematical aggregation convention. In this article, I try to revise the theoretical debate on aggregation rules by looking at contributions from both voting theory and multi-criteria decision analysis. This cross-fertilization helps in clarifying many ambiguous issues still present in the literature and allows discussing the key assumptions that may change the evaluation of an aggregation rule easily, when a composite indicator has to be constructed. (Contains 9 tables and 11 footnotes.)