This phrasing suggests you may misunderstand the nature of the market at a fundamental level - the market itself never does anything. Firms within the market may do this or that. The market is simply the relationships between actors over time - it is completely ephemeral and has no real existence and cannot do anything.
Let me try a different tack in answering your question - I think you are confusing several things together that are best reasoned about separately, in turn:
- The market
- The market in law services (legal advice, arbitration/mediation, etc.)
- The law
- Philosophy of law
- Industry-standard legal practices
The market - as already mentioned - is simply the relationship between actors over time, nothing more. Hence, the market does not produce law, it does not enforce law, it does not evaluate standards of legal practice, and so on.
The market in law services is that portion of the market (insomuch as it is not completely monopolized by the State) which specializes in the production of law-related services such as giving legal advice or mediating/arbitrating disputes. It may also - as David Friedman theorizes - be “bundled” with protection services and sold to consumers as a bundled package. To a very tiny extent, the current state of the world with many nations that a person could, in theory, choose to reside in acts somewhat like this market, just with extremely high switching costs and with certain switches being prohibited (not just anyone can become an Israeli citizen and vice-versa) altogether and with a very limited selection of firms which also happen to have territorial monopolies.
The law is something that stands above and beyond what anyone may write about it. Despite the fact that we refer to them as the law, statutes certainly are not the law, at least, not when they’re first written (they may infuse into the culture over time and become law, however). The “packages” offered by Friedman’s hypothetical protection agencies would not be the law. The positions and opinions of arbitration courts would not be the law.
The law - like language itself - is not up to anybody. Oxford can write its dictionary, the King can speak his English and the Atlantic can look down their grammatically-correct noses at the rest of us but, at the end of the day, the English language is whatever people use it to be. Like the law, it varies from place to place and time to time. Similarly, the law is whatever the norms are “out there” that individuals will actually accept in the resolution of their disputes.
Those norms are discovered in the process of settling real disputes. The mechanics by which disputes get settled are immaterial - whether it involves protection agencies or not, whether it involves arbitrators or not, whether it involves aggression insurance (Hoppe) or not. All that matters is that a dispute arose, it got settled, and there were some terms by which it was settled and the settlement either stuck or it did not. Those are the only really important parameters to uncovering the normative content of the law.
The one thing I dislike about Friedman approach to analyzing the law market is that it obscures the role of the individual by starting the analysis with the firms (protection and arbitration agencies). Because Friedman’s protection agencies are trying to sell their services to customers, what those agencies offer as bundled “law” is ultimately up to the consumer, that is, the individual. However, it does have the advantage of being a kind of “superset” of the existing order which makes it easier for people to comprehend the conditions for its realization.
Philosophy of law is the subject that is concerned with explaining everything I’ve written above and, ultimately, with answering OP’s question. The philosophy of law has to do with discovering what are the essential or constitutive features of law (what is law versus non-law), generalizing the particular normative contents of law and developing justifications for legal practice, that is, answering the question “what is the right way to do law?”
Industry-standard legal practices are what emerge out of the market in law. Just as cellphone makers are all driven by consumer demand to include texting features in their phones or whatever, so producers of legal services are driven to conform to social norms* (that is, the law) and legal practice (including things like standards of evidence, trust and verification protocols, and so on).
OP’s question is a question about industry-standard legal practice in the absence of state monopoly of law that should be answered by the philosophy of law. (Sorry this post is so long but the entire thing is necessary to give a proper reply).
Questions such as “what are the proper standards of evidence for deciding questions of fact?” hinge on both the philosophy of law (specialists who provide analysis of the relative merits of the best known standards) and industry-standard practice (the extent to which real arbitrators actually listen to the philosophers).
There is no simple answer to your question “will ‘preponderance of evidence’ be used in the free market in law” - I think the answer could depend on the kind of question of fact that is under consideration, it depends on how “preponderance” is evaluated or whether it can be evaluated at all, the nature of the evidence (tained by conflict of interest, coercion, blackmail, etc.) and so on.
If you want to get an idea of what I’m talking about, take a gander at the Rules of Civil Procedure in the State of Oregon. Most of these rules are not set by the legislature (they just get rubber-stamped), they are set by the judiciary. And when you read the nature of the rules, you will realize that they are, by far, more important than any particular legislative rule because they determine the conditions under which such rules can at all be applicable! It doesn’t matter if you can be sued by the State for such-and-such petty reason if the Rules of Civil Procedure determine that the evidence in your case is inadmissable. The Rules of (Civil, Criminal) Procedure are the law’s law.
Clayton -
*This is another deficiency in Friedman’s exposition as his gives the impression that social norms can be arbitrarily chosen and he illustrates this with the somewhat compromised illustration of a pro-death penalty versus anti-death penalty protection agencies/arbitration