Nondictatorially independent pairs and Pareto

Suppose a social welfare function f has complete and transitive values and the set X of outcomes has size m>3. If the domain D of f has the free quadruple property then the fraction of pairs on which f satisfies nondictatorship, independence, and Pareto is less than or equal to $\left (\displaystyle {1 \over m^1/2} + {1 \over m - 1} \right)$.