A social welfare function is Arrovian if it is transitive-valued and satisfies IIA. We examine the logical relation between the statements (A) If f is Arrovian with domain F then it is dictatorial if it satisfies the Pareto criterion and (W) If f is Arrovian with domain F then it is dictatorial...

The set of alternatives is infinite. If social welfare function f satisfies the Pareto criterion and there is a positive integer [beta] such that for each pair of alternatives, {a,b}, there exists a set S(a,b) of at most [beta] alternatives such that a and b can be socially ordered on the basis...