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I'm not saying it would be the right way. Of course both sides will accuse each other of cheating (and they'll probably both be right!)
The point is, if Greenland holds a referendum that comes out in favor of joining America and America says "Welcome aboard!", nobody else is in a position to meaningfully object.
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It seems like the obvious course of action is to hold a local referendum after making a sweetheart offer. If the Greenlanders vote to join the US as a territory, no one else would have any grounds for objection.