If a person has something stolen the judge would proceed as follows. He would undertake an investigation to discover the thief. He might employ an expert to assist with the investigation. In a free society, many private investigators would be available. Some would operate on the basis of only receiving payment if the thief is brought to justice. This might cost more, but the victim would be able to pay the investigator out of the restitution received.
When the thief has been identified, the victim will confront him. If he confesses and returns what has been stolen, that would probably be the end of the matter. If the thief refuses to confess, the victim will take the case to a judge.
The accused thief has two options. He could agree to take the case to a judge. In this case they victim and the thief would need to agree on the judge and they would agree to accept his decision. Both parties would want a judge who had a reputation for honesty and wisdom.
The other option for the accused would be to refuse to go to accept any judge. If he does not submit to the judge, he will come under suspicion and people will stop trusting him. Life would get very difficult as people in the community would be reluctant to buy things from him. Refusing to submit to a judge would probably more expensive than making restitution.
If the accused refused to submit to a judge, the victim could still take his case to a judge. He would want to avoid any suggestion of bias, so he would choose a judge who had a reputation for being fair to thieves. He would avoid his friends or anyone who might be accused of favour him.
The accused would present his case to the judge. To preserve his reputation for fairness the judge would check the evidence very carefully. Even if the accused refused to appear before him, the judge would look for all evidence or alibis that might favour the accused. He would bend over backwards to be fair, as this would be the best way to maintain his reputation. A good reputation is essential for a judge who wants to continue in the business.
If the judge decides that the accused is guilty, he would specify the amount of restitution that must be paid. This would usually be for times the amount that was stolen. If the thief had submitted to the judge, he would effectively have contracted to pay the amount specified by the judge. When the restitution is complete, the judge will advise the community that the thief has paid his debt.
If the thief was dishonest, he might refuse to pay what he owed, even if he had submitted to the judge. The solution is the same, whether the accused had submitted to the judge or not. The judge would announce to the community that the thief had been convicted, but refused to pay.
The people of the community where the criminal lived should support the judge by refusing to trade with the thief until he has paid the specified restitution. His employer might take a percentage out of his wages to go towards the restitution. Other employers could refuse to employ him. If everyone refused to buy from him or supply him with goods, he would eventually have to have pay restitution just to survive.