A social decision function operates on individual weak orderings to produce acyclic social preference. The structure of a general neutral monotonic SDF is studied. It is shown to be characterized by the veto, if individual indifference is banned. With such indifference present, the characterization is by a veto structure, a hierarchy embracing all individuals. The reason for the interest in acyclicity [21, 22] is that it averts the voting paradox, permitting a choicefrom each subset of alternatives. This is for the finite case. When that assumption is dropped, an infinite ascending sequence of preferences prevents a choice. It is shown that this last phenomenon need not be prohibited along with cycles; the absence of such social sequences is implied by their absence from individual preferences.