A social welfare function $f$ is Arrovian if it has transitive values and satisfies Arrow's independence of irrelevant alternatives condition. For any fraction $t$ and any Arrovian social welfare function $f$, either there will be some individual who dictates on a subset containing at least the fraction $t$ of outcomes, or at least the fraction $1 - t$ of the ordered pairs of outcomes have their social ranking fixed independently of individual preference. If individual preferences are strong, we can say more: Associated with any Arrovian social welfare function, there is a set containing a large fraction of citizens whose preferences are not consulted in determining the social ranking of a large fraction of the pairs of alternatives. (The Pareto criterion is not assumed.)