That's a bold statement, A.J. What's the difference between minarchy and anarchy?
You seem to be assuming that no social contract means no government. I don't agree with that. See #s 63, 69, and 71.
In fact, it seems to me that basing your government on any meaningful form of consent leads in a straight line to anarchy. I haven't seen an adequate reply to the anarcho-capitalist critique of tacit consent. Even if you go live in the woods, civil society will come after you for endangering a species. Locke's majoritarianism presupposes everyone agrees to be in civil society in the first place. If I don't agree, why should I be concluded by the majority of that civil society I never joined any more than I would be concluded by the majority of Frenchmen? If membership in civil society really does depend on consent in any meaningful way (not, that is, once in always in, and being born is considered tacit consent to enter), then any one person or group of persons can unconsent at any time, and what that leads to is Rothbardian secession: states have the right to secede, and if states have that right, so do counties, and cities, and neighborhoods, and blocks, and individual residents.