In talking about Covenental Anarchy it is helpful to give some definitions so that it is clearer what I think I'm talking about.
A covenant is a clearly-defined relationship in which there are mutual obligations. For this, I take as the example the many covenants which are "cut" in the Old Testament, primarily between God and Israel. It is an agreement of mutual obligation and, theoretically, mutual benefit. Both sides agree to it with knowledge of what it is they are agreeing to, and what will be expected of them.
One thing that is key to consider is that a covenant does not exist without consent. You can't be forced into one - though one might argue that you could be born into a covenant, in the sense that it is up to you to leave it if you choose. That also might change depending on the covenant one is considering (i.e. both Judaism and Christanity have rituals around a person accepting their part in the covenant community)
The covenant is whatever the people involved decided it is. It is worked out ahead of time and then binding commitments are made. It should be beneficial to both parties because the punishment for failing to live up to the covenant is nothing more than not being part of the covenant anymore.
I model my thinking about this kind of covenantal relationship on what I understand to be how God relates to us, and how we are admonished to relate to each other by scripture and the witness of the early church. More on this later, however - I don't want this post to be too long.
Anarchy is simple - no archy, no rulership, no dominion. I don't use a dictionary definition here because I find that dictionary writers often assume that governmental authority is a good thing in a person's life, and I don't agree that it necessarily is.
If you think about non-dominion for a bit, you might realize that violence is entirely out of the question. Every archy, every dominion, relies on violence (with the exception of one - we'll talk about that later). The reason for this dependence on violence is that, at some point, there will be a conflict. In a dominion system, it is the power at the top that holds the monopoly on violence used to enforce its will on those beneath. We negotiate with any given government how much of our free will we will let the government override in exchange for the protections or conveniences that we believe that government offers. Political conflict sometimes boils down to haggling over the price of our autonomy.
The insight I feel like I've received as a pacifist who reads the works of other pacifists and talks to other pacifists is that if we discipline ourselves to choose anything other than violence, then we have to rethink things like authority and autonomy entirely. What I find is that dominion as we tend to practice it now just doesn't work unless there is violence hanging over everyone's head.
So I go looking for another way. Thankfully, there is one dominion, at least, which I believe does not depend on violence - which in fact has as one of its core teachings the absolute rejection of dominion through violence. That dominion is, of course, the dominion of Christ, and that absolute rejection of dominion through violence is demonstrated decisively in the crucifixion and resurrection. Among many other things, these events demonstrate God's commitment to not use violence to enforce dominion under any circumstances - even in defense of the life of God's son.
I find this very reassuring. I call this dominion of God as demonstrated by Christ covenantal anarchy, and I am continually excited to see where it leads us.