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No police means crime is unregulated.
The reason we have police is because the government has taken away guns and the right to defend themselves against criminals from the people.
People can defend themselves against crime, they don't need police.
By that I don't mean that they don't need organization. Organization is often a good tool to fight crime with, and an in anarchy I predict that people would band together to fight violent criminals.
The police spend most of the time arresting prostitutes and weed sellers anyway, and they aren't really that affective at stopping murderers, despite what America's Most Wanted would like to have you think.
I could also argue if I wanted to really heat things up, that the state is the cause of this violent crime in the first place. (Don't respond to this paragraph, I won't defend it, I'm not arguing it).
When we hear about anarchy, the truth often is that the rule by a police state has been temporary superseded by rule by the gang state. They're both the same, except the police try to be civilized about it.
ADDITION:
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YOU DO NOT HAVE ANARCHY AND ANY SORT OF CIVIL SERVICES. THAT IS NO LONGER ANARCHY.
I agree 100%. It really annoys me when left wing libertarians try to pretend they're anarchists. They're not, they're just stupid posers who give real anarchists a bad rap.
Real anarchists are against things like gun control.