Now you might be wondering "Wouldn't companies just rule in favor of whoever payed them the most? Wouldn't poor people be unable to afford legal protection? Wouldn't that make the law impossible to enforce since a rapist could refuse to go to any court that wasn't run by MRAs? Wouldn't the competing police forces/courts inevitably clash with each other and cause a civil war, the winner would be a new government?" The answer to these questions is "NO, BECAUSE IT JUST WOULDN'T SHUT UP!"
disclaimer: I'm not an ancap. I don't necessarily believe these answers, but they are my best guess of what an ancap would say.
Wouldn't companies just rule in favor of whoever payed them the most?
If your company was known to be biased like this, people who expect to be innocent would not want to hire it (because they expect to be innocent and don't want to pay extra for rulings in their favour). Further, if I know you hire companies that will rule in favour of the highest bidder then I won't interact with you, including trade, and you will lose money.
Wouldn't poor people be unable to afford legal protection?
I think the two standard arguments are 'there would be less poor people in ancapistan' and 'it's not like the current system doesn't fuck the poor anyway, we'd still be a strict improvement over it'.
Wouldn't that make the law impossible to enforce since a rapist could refuse to go to any court that wasn't run by MRAs?
A condition for me interacting with you is that we'll both have some sort of corporation whose rules we both agree with. If rapists refuse to be bound by the rules of a corporation that bans rape, then they will be expelled out of every private space run by people who are against rape. They can go live in their little rapist utopia along with people who want to live alongside rapists.
Wouldn't the competing police forces/courts inevitably clash with each other and cause a civil war, the winner would be a new government?
War is very costly and rational organizations will attempt diplomatic solutions over violent ones, unless one organization is overwhelmingly more powerful than the rest (in which case that organization is the government, and you're not living in ancapistan).