A zero government society will come into being only after the entire population has been taught (by TOLFA or an equivalent) that each person owns him or herself absolutely, and so has no claims on anyone else; that he is responsible for his own life. From that follows the non-aggression principle, and since all will have embraced it, I anticipate a steep reduction in the incidence of krime - and of course crime will not exist at all, since crime means the breaking of laws and there won't be any laws since there won't be any government to write them. So altogether, the number of disturbances to the harmony of society will drop like a rock.
Even so, we can't assume it will fall to zero, and so a justice industry will arise - in response to market demand. Firms specializing in krime detection, kriminal apprehension, trial and disposition will all be players in that market and will, as always, be far more efficient than the present government monopoly. That is incidentally one of the few big errors in the vision Ayn Rand developed; she thought the market could not handle that need, for she supposed a single "final arbiter" would be required. Not so.
We've often referred to justice in editions of the ZGBlog, but this one attempts to pull together an idea of what that industry will probably look like. Freedom being essentially unpredictable, I'll certainly be wrong in some respects; but a set of reasonable guesses may be better than nothing.
"Justice" is defined as the restoration of lost or damaged rights, to the extent feasible. That is seldom the case today; more often it's seen in terms of punishing breakers of government laws, sometimes savagely. When Ross Ulbricht was found to have facilitated the prohibited drug market, he was sentenced to 40 years in a cage; yet there was no victim at all who had suffered the loss of rights. In the coming ZGS, though, that will be the only basis for a claim, and if the victim and the aggressor cannot agree on a settlement, that will be the only basis on which a court company will accept and judge the matter.
The particular court will be chosen by the victim, the plaintiff, and the company running it will prosper to the degree it builds a reputation for fair and wise decisions. If the aggressor fails to show, judgment will be recorded against him and that fact, together with his response (did he pay the ordered compensation?) will be published and anyone considering hiring him or trading with him will refer to that record and act accordingly. That will form his powerful incentive to attend the hearing and to pay what it orders. The court's fee will be paid by the plaintiff, but if he prevails it will be added to the compensation total.
Should the loser then refuse to pay it, that fact will be known and he will have a hard time even buying food to eat; he will be shunned, ostracized. That will be the ultimate sanction of the ZGS; he will have violated its only rule (not to aggress) and so will be repudiated by every member. Otherwise (if he honors the verdict and pays the compensation) the confict will be over; rights will have been restored, the only debt discharged, and both parties will continue life normally with the respect of everyone.
While the industry will be open to and designed for individual plaintiffs, I think insurance companies will play a large part. Krime will be so infrequent that a policy that compensates victims at once will cost very little; then, the position of plaintiff will be taken on by the insurer, who will go to court and recover what he can from the aggressor. This would bring early closure to the victim, and protect him from the problem of an indigent perp. A good bargain.
Always, claims brought to any court will be for restitution (the restoration of the lost or damaged rights) and never for retribution or punishment; the latter will be consigned to the History of the Government Era, for it has no place in true justice as defined above, despite its long popularity in state monopoly systems. Once a right (to property, an uninjured body..) has been restored to what it was before the aggression took place (or with court-ordered compensation if that is impossible) any additional burden imposed on the perp would reverse the matter; the victim would become an aggressor! The self ownership axiom provides that we own ourselves only, not anyone else in part or whole. Punishment presupposes an authority that has been offended; in the ZGS there will be no such authority.
In that regard I believe that Murray Rothbard made one of his very rare errors, for in his otherwise superb Ethics of Liberty he lapses into a commendation of punishment in "libertarian law" (an oxymoron!) provided that it's proportional and that it's directed to the benefit of the victim (see its pages 91 amd 92.) Part of the error seems to be his reluctance to abandon the term, for he does focus correctly on restitution, but confuses the matter with such as "...our theory of proportional punishment - that people may be punished by losing their rights to the extent that they have invaded the rights of others - is frankly a retributive theory of punishment, a 'tooth (or two teeth) for a tooth' theory."
"Two teeth"? No, never! And the use of the P-word fogs the matter. Justice demands only the restoration of the victim's rights, period; those certainly include compensation for his costs of bringing any action needed, and of the emotional distress he suffered, but nothing else. A penny less, should he be inclined to forgiveness, but never a penny more.
There are plenty of snarky questions that might be asked about the standard of justice outlined here, including the obvious one: wouldn't this give nasty rich people a pass? - that a wealthy sociopath could commit murder after murder yet pay up each time then continue his style of life?
My answer to that: yes, it would. But every transaction of murder and compensation would become public knowledge; his pattern of behavior would be an open book, on the Net. Would you want to do business with him, or to be his friend, knowing you might be next? I think he would swiftly plunge into a very lonely life.
To other such objections, there's no space here to list or answer them all, except to say that no system of justice is likely to be perfect. But one of this kind, with its sole aim of restoring rights, its competitive nature as an industry, and the visibility of its judgments, is optimal. In a real world, there can be nothing better.