The EU and federal states face the same dilemma: Effective problem-solving requires system-wide policies whereas constituent unit autonomy requires decentralized policy-making. Both the EU and federations cope with this dilemma by shared policy-making of centre and constituent units. Exit specifies the extent to which constituent units are subject to system-wide policies, while voice describes the influence on system-wide policies. Shared policy-making enables federations to differ in exit and voice, with varying degrees of autonomy for the constituent units. First, the extent to which constituent units opposing a policy have room for manoeuvre through exit depends on the degree to which they are indispensable for effective system-wide policies. Second, the degree to which constituent units influence decision-making on system-wide policies depends on the importance of the ‘federal diversity’ norm to the actors. The cases are educational policy, internal security and social policy in Canada, the EU, the US and Switzerland.