This again?!?!?
Check here. The question was slightly different, but the underlying problem is the same:
In “Libertopia” all land is presumably owned by someone. These someones have PDAs/Insurance/protection/ Agencies and agreements between them and between themselves and other individuals. Most (all?) of these arrangements would probably prohibit offering safe harbor to fugitives, aiding/abetting fugitives, etc. Also, since many people are afraid of fugitives, it stands to reason that they’d be more than happy to assist in their apprehension. This could easily be accomplished by laying siege to the fugitive if he didn’t want to submit to arbitration/dispute resolution. Fine: he can suffer house arrest in perpetuity. This is easy to facilitate, because land is not public, and those people who live on adjacent lands will likely be unwilling to give him free passage. They, or their agents, will be happy to apprehend him coming or going, or to prevent people from giving the fugitive aid and comfort.
So, the longish-short answer is that it may not be necessary to use “force” as it is contemporarily conceived, i.e., masked men break down the door in the middle of the night, handcuff/hogtie the accused, and drag him off against his will to prison where he’ll be tried by 12 men who were too stupid to get out of jury duty, etc.
They could simply wait for him to arrive upon another’s property, and take him then … Most people probably couldn’t survive locked inside their own house for more than a week. Sooner or later, most people would submit to arbitration.
But, you’re also asking, “How do we determine who ‘A’ is?” That’s a different question than “Once we know (or presume to know) who the perpetrator is, how do we deal with him?” which is what I try to answer, above.
The answer to your question may not be entirely satisfactory, but then again, you’re asking lifeboat questions.
The goal in a free society is to A) prevent these crimes from occurring in the first place, and B) to compensate the victims accordingly in the event that the agency fails to protect them. Now, of course we can’t prevent all murders or all home invasions, but many of them might be prevented. Of those that slip through, we won’t be able to solve all of them, but there’s not any good reason to presume that a free market would be worse at crime solving than the State. Is there?