No one can mention any real life examples of both theories and that is because they are fictional theories.
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Socialism assume that companies could work with no centralized ownership which is impossible in real life, it’s like the believers of this theory ignore all the human psychology and assume the perfection in the world.
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Anarcho-Capitalisim assume that it’s possible to live in 100% autonomous society while ignoring all the big issues(unfair laws, corruption in law and protection agencies, …etc)
Name me a single time it’s been tried without US interference.