Under anarcho-capitalism, you'd still have courts and police. They would be cheaper and more effective and if they weren't you could chose a competing provider. You can't do that today.
I guess which mafia you'd "choose" would depend on which one was pointing a gun at your head at a given point.
Having courts and police means having government!!! As soon as you have a court and enforcement system, you've effectively decided to have a government.
It's true that mafias and militias also enforce their own courts within their "territories" - but these tend to be more expensive than normal government.
And only the lowest IQ person would think they'd have a "choice" about which mafia's rules they would follow in the absence of a govt. You don't believe all that hippy dippy stuff about rival militias not trying to enforce their will over you because they believe in peace and love and doves and stuff, do you?