Most people I’ve spoken to don’t believe that reliable courts could emerge from free markets, and I admit to being pretty unsure about the prospect myself despite being a libertarian.
But an Economist piece on international law provides at least weak evidence that a society with no State, or a severely weakened State, could still come up with legal services.
Apparently huge amounts of international law is handled by the legal systems of just two countries: America and Britain. This is partly because both of these countries have centuries of common law and strong legal precedents, meaning the rulings produced are relatively secure. Adding to the mix are centers of arbitration for international parties with cross-border disputes that have emerged in Singapore, Hong Kong, and elsewhere.
Bear in mind that there is no supranational governmental body determining which countries’ laws will be held as the international standard. Rather, over time certain legal systems have been judged superior, and when India has legal issues to settle with China, both countries opt for an American court or an arbitrator in Singapore.
The analogy isn’t perfect, but I don’t see why the same thing couldn’t happen on a smaller scale, in individual countries, as a result of market processes.