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Something like your takeover scenario already happened, but not through AI. It happened through atomic weapons.

Nations who have them are in a different class from nations who don’t. Nations who have a lot of them, delivery systems, and systems that might be able to shoot down some of a counterattack are superpowers.

Using this leverage these nations and their leaders have been able to dictate world policies. Through the last half of the 20th century this was the US and the USSR. Now it’s the US, EU, Russia, and China, and a few smaller nations with a few nukes. The club is a little bigger but not much.

This kind of thing could happen in the 21st century with AI. If so it will probably be the US and China who control the most powerful AI “agency amplifiers.”