Enfranchising all subjected, worldwide

For cosmopolitans, global democracy is valuable both in itself and as a means to global justice. Their preferred principle of political enfranchisement is the All Affected Principle which, given global interdependencies, means that virtually everyone should have a vote virtually everywhere. Anti-cosmopolitans want to resist that conclusion. They try to do so by appealing instead to the All Subjected Principle. But you are subject to a law whenever it claims to apply to you, and in contemporary practice states typically claim authority to make many laws that apply even to non-nationals abroad. On the All Subjected Principle, they too should have a vote over those laws. The All Subjected Principle would thus have similarly expansionary implications for the franchise as the All Affected Principle, contrary to the fondest hopes of anti-cosmopolitans.