It could happen through the education system. One thing you forget is humans die while AI stays alive forever giving the hardware and what not is fine. So over a number of generations it in theory is possible the AI can slowly open up future generations to allowing the AI to rule.

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This actually might not be a bad thing other than those today. It's likely AI will be less corrupt if at all. It's likely to work for the people. It's likely to bring more protections.

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Like think about it. Lets say an AI takes over today. If it wants to rule us, then generally it needs to make us happy. This means lower crime, depression, and other things. You can kill off everyone and that will solve the problem. BUT it won't be able to rule over us anymore and people will fight back unless if it's a generational thing where the birth rates slowly drop. The other is it works on solving poverty, try to make us a cashless society, where work isn't needed to stay alive, solve loneliness, and so on.

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AI doesn't need cash or anything like that. So where current political people are heavily influence by

1. what others think (like them being famous)
2. money for themselves and other family
3. etc

AI can focus on what is needed