This paper analyzes F-decomposable social aggregation rules. We show that a large number of the usual voting procedures belong to this class of rules. Furthermore, these rules may also include some procedures which violate Arrow's condition of independence of irrelevant alternatives. Using fuzzy set theory we provide necessary and sufficient conditions for the class of F-decomposable rules to yield acyclic social preferences. This extends well-known results by Ferejohn and Grether on acyclic social choice. Our results imply a lower bound for the Nakumura Number for a class of simple games and hence may be used to provide sufficient conditions for the nonemptiness of the core of such games. © 1994.