A more thorough explanation:

Private judging is a type of alternative dispute resolution where the parties involved in a case hire a private individual to hear and decide the case. This process can happen as a matter of contract between the parties or in connection with a statute authorizing such a process. It is also known as rent-a-judging.

Unlike arbitration, private judging is a less contractual and less privatized process. The parties have the freedom of contract to determine the time and place of trial, as well as the identity of the judge. However, privately judged trials may be required to use the same rules of procedure and evidence used in ordinary litigation, exposed to public view by court order, adjudicated only by a former judge, and subject to appeal in the same manner as other trial verdicts.

Two parties, John and Jane, are in a dispute over a contract. They decide to use private judging to resolve their dispute. They hire a retired judge to hear their case and make a decision. The judge follows the same rules of procedure and evidence used in ordinary litigation and makes a decision that is subject to appeal in the same manner as other trial verdicts.

This example illustrates how private judging works. The parties involved in the dispute hire a private individual to hear and decide their case, and the process follows the same rules as ordinary litigation.