Ok, I can see the appeal of "free-market-conflict-resolution", however, each "conflict-resolution-organization" (CRO) would also need an enforcement arm. For example, if party A subscribes to CRO#1 and party B subscribes to CRO#2 and they can't agree on which CRO should handle the case, each insisting that their personally subscribed CRO arbitrate their disagreement, then CRO#1 and or CRO#2 must resolve their conflicting conclusions, either by FORCE, or by mutually agreeing to another CRO#3 in order to resolve the dispute resolution between dispute resolvers (CRO#1 and CRO#2).

Ultimately a hierarchy of CROs would emerge, and perhaps some balance of power might exist between two or three CROs for some period of time, but eventually a single CRO would either coerce or FORCE the others into de facto submission, thus becoming the Supreme CRO, The Supreme Court so-to-speak, or, The Ultimate Arbiter Of The Law (TUAOTL).

A system like this already exists. Two parties can agree to an "out-of-court-settlement" by agreeing to a mutual arbitrator. A law firm is a de facto CRO and there is a "free-market" of these CROs. The CROs with the "best" reputations charge the most money for their services. This has the effect of insuring the wealthiest citizens get the most favorable outcomes.