So now you've changed the question. Fine. I'll answer this one, then you answer mine.
The plaintiff in your scenario (the State Prosecutor) does not get to choose the Judge. Are you familiar with our legal system at all?
As far as what the State does when one party refuses to arbitrate, it depends on who is refusing. The prosecutor can drop charges if they don't feel confident in getting a conviction or they can file an arrest warrant if the defendant fails to appear in court.
It's no secret how this works. You could have just looked it up instead of talking in circles.
So how about answering my question now? If both parties must agree to the arbitrator, what do you do when one party refuses?
I am intimately familiar with the empire's legal farce. Also the fact that the plaintiff (prosecutor) doesn't choose the individual judge
doesn't mean the plaintiff and the judge don't work for the same entity, because they do. They both work for the state. Your assertion that they are separate is a fallacy. Do you really want to argue THAT point or just concede it ?
A question for you - What recourse does the accused have if he has no choice in who will arbitrate in the present legal paradigm?
This is a partial answer to your question....I could go on, but you'll need to admit that in the present paradigm the accused has no real recourse when the state is BOTH the plaintiff and the judge / court / supposed neutral arbiter.
The following is an excerpt from The Market for Liberty....enjoy.
As in the case of contractual disputes, the threat of business ostracism would usually be enough pressure to get the dispute submitted to arbitration. But occasionally the accused might want to refuse arbitration; and he could be guilty, or he could be innocent. If an accused man were innocent, he would be very foolish to refuse to submit evidence of his innocence to representatives of the arbitration agency and, if necessary, defend himself at an arbitration hearing. Only by showing that his accuser was wrong could he protect his good reputation and avoid being saddled with a debt he didn't deserve. Also, if he could prove that he had been falsely accused, he would stand a very good chance of collecting damages from his accuser.
If, however, the accused man were guilty, he might refuse arbitration because he feared that the arbiters would rule against him. If the accused did refuse arbitration and the injured party had good grounds for his case, he could treat this recalcitrant disputant just as he would treat a man who had stolen something from him — he could demand repayment (for details of how he would go about this and how repayment would be made, see chapters 9 and 10).