We’re about to enter our 19th consecutive year of Truman-envy. Ever since the Berlin Wall fell, people have looked at the way Harry Truman, George C. Marshall, Dean Acheson and others created forward-looking global institutions after World War II, and they’ve asked: Why can’t we rally that kind of international cooperation to confront terrorism, global warming, nuclear proliferation and the rest of today’s problems?
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Groups with a strong narrow interest are able to block larger groups with a diffuse but generalized interest. The narrow Chinese interest in Sudanese oil blocks the world’s general interest in preventing genocide. Iran’s narrow interest in nuclear weapons trumps the world’s general interest in preventing a Middle East arms race. Diplomacy goes asymmetric and the small defeat the large.

Moreover, in a multipolar world, there is no way to referee disagreements among competing factions. In a democratic nation, the majority rules and members of the minority understand that they must accede to the wishes of those who win elections.

But globally, people have no sense of shared citizenship. Everybody feels they have the right to say no, and in a multipolar world, many people have the power to do so. There is no mechanism to wield authority. There are few shared values on which to base a mechanism. The autocrats of the world don’t even want a mechanism because they are afraid that it would be used to interfere with their autocracy.

i'm not convinced a League of Democracies is the answer because it is not remotely apparent how that would be any different from another talking shop
the main problem is as the article points out small groups having a veto power

the example of the Irish No vote is a good example -- we have many many shared values across Europe and have a League of European Democracies but that didn't stop the Irish blowing progress out of the water by taking a very narrow blinkered approach

finding consensus in a multipolar world is a fundamentally difficult problem and unless and until we have a global government will remain so
the only way forward is through pooling sovereignty and by surrendering the right to veto and nation states are notoriously loath to do so
(after all you Americans ended up having a civil war over the issue of federal rights versus state rights -- centralization v decentralization )