They should behave as ministers of divine providence. What we are talking about here, of course, is the principle of subsidiarity. In political theory, it takes the form of the axiom that the most local level of an organization which is capable of handling a certain issue should have the authority to handle that issue. Subsidiarity is the guiding constitutional principle of the Church. It is the reason why bishops have such wide discretion over matters of discipline and liturgy in their own dioceses.
Subsidiarity has applications far beyond ecclesiology.
It is closely akin to the principle of federalism in American constitutional theory, under which the states are supposed to retain primary jurisdiction over government functions that are local by their nature. The European Community explicitly defines the relationship of its member states to the union government as one of subsidiarity. What we should note here is that the principle does not just protect the rights of local jurisdictions. It also strongly implies that hierarchy, properly understood, is a positive good. It sets limits for state intervention.