This is the kind of thing my OCD brain doesn't let go of.
Then the usual arrangement of policing and courts in stateless (and minimal state) societies will keep you going for a while;
everyone in the society is insured against torts (there are generally no "victimless crimes", or if there are some, they are very few in number and small in scope, if the prudes had to pay entirely out of their own pockets for let's say banning drugs, drug prohibition wouldn't last very long. It's only because the state provides a mechanism for the prudes to socialise the cost of enforcing their intolerance onto everyone else, via taxes, that idiocy like a war on drugs exists).
no one who suffers loss or injury goes un compensated, even if the perp is a minor, mentally ill or flees. Now, admittedly, money isn't going to make you whole again, but there is a price point at which you and your supporters are going to take the money rather than go after the perp.
Historically, there have been different ways of organizing the insurance, and it has generally been "mutual". In Medieval Ireland it was people who cooked and ate together (Kitchen groups), Anglo Saxon England, it was neighbourhoods, in present day Somalia (the Somali customary legal system has potential to be the finest in the world!), it is by the offspring of a common great grandfather. In Medieval Iceland, it was pretty much a free market, you could contract with anyone else on the island, and you could sell a tort claim on, for someone else to pursue the perp, just like you can sell a debt.
In each case people can apply to join a different insurance group, and those who are repeatedly the source of claims risk being expelled and unable to function in society (there is a business opportunity there for offering those people protection in return for a much higher price - a sort of self funding voluntary open prison).
Move that into a present day setting, and most people would probably go for a competing for profit commercial insurance companies, but that certainly wouldn't exclude other possibilities such as mutual, fraternity, labour union, or church based insurance groups. (take the state and licensing out of the equation and you can expect an extremely competitive and diverse market).
The insurance group provides the police for your defence and legal defence in a court.
in the event of a claim against you, your insurer has the job of bringing you before a court.
Now imagine a market for private competing courts - to resolve disputes.
Such courts are actually present now, in the form of the arbitrators specified and agreed upon incase of dispute in business contracts - because the state sector courts are too slow, too expensive and are very unlikely to even understand the issues involved.
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This will get you started, it's not perfect, but it is extremely good;
Link Removed
Benson's book, that the linked piece is a short excerpt from, is about 400 pages long and has from 60 to over 120 refs cited per chapter. Plenty to get your teeth into, but it's difficult to convey all of the arguments in the short space of a forum post.
or at least a forum post that anyone can be bothered to read.