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In David Friedman's model, all, or almost all, enforcement organizations and courts will have relationships with each other to contractually resolve disputes, which works well enough and naturally enough if the number is not unreasonably large. These contracts create the law and the legal system, thus most law derives from explicit or implicit contract, contract to which particular identifiable people have explicitly consented.
The trouble with this model is that insiders, established organizations, might quite likely refuse recognition to outsiders, new competition, leading to cartelization. In Iceland, law and judgement was cartelized, but force was not. This worked quite well when the number of people in the legal cartel was large, but when the number of organizations in the cartel became small, things fell apart, as each saw kingly power within reach, and tried to get it before someone else did. In the eleventh and twelth century in much of Europe, both law and force was cartelized, with a few people privileged to bear arms, and the great majority powerless and afraid. This worked very badly for those that were disarmed.
David Friedman's model relies almost entirely on contractually generated law whereas Rothbard's model, with few or no explicit contracts between organizations, relies primarily on natural law. Seems to me that there is a role for both forms.
If you catch a burglar or a mugger, you do not need no stinking contract to give you the right to deal with him. If, however, you have a disagreement with your neighbors about fences, or common drains running under several properties, you do need a pre-existing contract, or at least pre-existing practice that provides an implied contract. So you deal with the car-jacker under natural law, taking account of the practices and concerns of his defense organization, if any, but without too much regard for agreements between his defense organization, if any, and your own, while you deal with your neighbor's fence under contractual law.
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