The need for services doesn't go away if the state goes away. I never hear any libertarian's or anarchists make this claim. The disagreement is usually around how the services will be provided. Security is pretty simple. Private security already outnumbers gov police in the US. Again, I recommend reading Bob Murphy's short book Chaos Theory. Its free and has good answers to these questions.
No one can say with certainty what a stateless society would look like but we know how the state uses force to oppress people. Most of the concerns about anarchy I read are descriptions of the current state of affairs.
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I need to read this book to try to understand how it would work. Who pays for the private security you propose?
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I mean is it that hard to imagine? We have subscriptions for everything these days. It could even be bundled into one service with other things. But, you would have multiple vendors and no "thin blue line" nonsense.
Bob simply goes through some possible approaches. Most would be related to insurance companies being regulators where things clearly need some sort of rules. Many government functions are legitimately valuable but poorly executed because of the monopoly and lack of a profit motive. I'm not on the top of my game today so I would refer you to Bob's short book vs. me trying explain it while dealing with a cold.
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