Intergenerational social choice without the Pareto principle (Q918349)

Let X be a set of 3 or more social alternatives and N a set of 2 or more voters. Two results are proved about a social welfare function f on X. If f satisfies nonimposition and independence, and N is finite, then f is either constant or completely dictatorial. If f satisfies nonimposition, independence, and continuity, and N is infinite, then f is again constant or completely dictatorial. The first result is given a new proof; the second is new.