It's not that there is no theft in Libertopia- the thieves just no longer have the luxury of calling theft "taxation". And, "taxation" was always the most common excuse for theft back during the "Age of Authority".
How is theft dealt with in Libertopia? Quite handily, thank you.
In fact, there are lots of people who get their inspiration from the Robin Hood of legend. He's the guy who retrieved stolen property and returned it to its rightful owner- even though I have heard that truth was perverted into "he robbed from the rich and gave to the poor" for a time. But not anymore.
Our robinhoods retrieve stolen property and return it to its rightful owner, and only ask for a small percentage of the value of that which is returned. And they only ask for that in cases where the owner can afford it. Although most people are so grateful to get their stuff back that they'd pay the robinhood even if he didn't ask.
The way this usually works is that arbitrators will put out a list of those who have refused to abide by the outcome of arbitration- or have refused arbitration at all. This list is used to inform others of people who they may want to shun, or publicize as untrustworthy. Some, such as the robinhoods, take a more active approach.
Robinhoods will look at the list and decide if any of the cases would be something they'd like to pursue. Most robinhoods limit themselves to stolen property cases, but some will take on other types of damage that resulted in a monetary judgement- that's just up to the individual.
In cases of stolen property, the robinhood will try to get the actual property back. If that's not possible, he will try to get something from the thief of equal value. This is then turned over to an arbitrator- preferably the one who oversaw the original dispute. The arbitrator then contacts the interested parties and facilitates an arrangement between them. The property may be sold and the theft victim paid, with any amount above that going back to the thief. Robinhoods try to be very careful to not go too far, lest they find themselves on the wrong side.
Sometimes the robinhoods will still find themselves called into arbitration on accusations of theft or trespassing, but unless the robinhood was unusually "zealous" in carrying out his job, the case doesn't normally go far.
As you may see, theft doesn't pay here unless you can hide what you have done so well that even people with expertise in solving the case can't find you. And that is extremely rare.