ARROWIAN CHARACTERIZATIONS OF LATTICIAL FEDERATION CONSENSUS FUNCTIONS

In this paper we begin the construction of an abstract axiomatic theory of consensus functions in order to account for several classes of similar concrete results in the domain of the axiomatic approach to consensus. Such results, which belong to various fields, are mentioned in our introduction and conclusion. Among the consensus functions defined on a semilattice L, i.e. the functions Ln → L, we study the federation consensus functions associated with cohereditary families of subsets of {1,...,n} called 'federations' (or simple games). We obtain several axiomatic characterizations of all federation consensus functions, or of significant subclasses of such functions, and especially of the meet projection ('oligarchic') consensus functions. These characterizations depend on the structural properties of the considered semilattice, which are the key to understanding the concrete results mentioned above and allow us to obtain new results. We end by pointing out some further lines of research. © 1990.