There are various private court/police structures that end up being socially efficient. You pick a police/court company and they have contracts with other polic

There are various private court/police structures that end up being socially efficient. You pick a police/court company and they have contracts with other police/court companies that specify how arbitration happens. It doesn't rely on any sort of goodwill or miraculous happenstance. The end result is not that much different from what we have today except you should get more for your money and you have some more flexibility in picking which rules you're subject to. The space of admissible rulesets is determined by the cost of negotiating contracts between your court system and the other court systems you might have to interact with.