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The best mechanism for democracy, whether at the level of the multinational state or that of the planet as a whole, is not an all-powerful Leviathan or centralized superstate, but a federation, a union of separate states that allocate certain powers to a central government while retaining many others for themselves.
Federalism has already proved the most successful of all political experiments, and organizations like the World Federalist Association have for decades advocated it as the basis for global government. Federalism is largely an American invention. For all its troubles, including its own serious bout of secessionism 130 years ago and the persistence of various forms of tribalism today, the U.S. is still the best example of a multinational federal state. If that model does indeed work globally, it would be the logical extension of the Founding Fathers' wisdom, therefore a special source of pride for a world government's American constituents.
As for humanity as a whole, if federally united, we won't really be so very far from those much earlier ancestors, the ones huddled around that primeval fire beside the river; it's just that by then the whole world will be our valley.