The Three Relations

There are three general types of relations, hierarchy, reciprocity, and communism. Each functions differently and are, generally, based upon the manner in which things flow. In hierarchy, things flow from those without power to those with power, in reciprocity, things flow equally both ways with each actor getting as much as they give, and, in communism, things flow freely from those who have more to those who have less.

Now, both relations of reciprocity and of communism have an implied equality between the two sides of the relationship. That is, in reciprocity, both actors are expected to bring the same amount to the table and the exchange is supposed to be equal, while, in communism, those who have more give to those who have less, in essence, acting as a balancing of an existing material inequality because of a relationship of equality.

Hierarchy, on the other hand, explicitly rejects the equality between the two sides. The person who is higher in the hierarchy is expected to get more than the person who is below, and not insignificantly, but often hundreds of times more. In addition, when things flow down the hierarchy, it's because they are lesser than that which is flowing up it. So a bushel of apples is given as tribute by the peasant to the king, and the king gives the rotten apples from the bushel to the peasant.

All relations can be seen as operating within one of those three very general frameworks, and they are also mutually exclusive in that, as a relation begins to exhibit one of those relations more and more strongly, the other two begin to be exhibited less and less. So, as an example, the relation between boss and worker begins as a relation of reciprocity. The worker offers their labor and the boss offers a wage. Exchange happens and each gets something out of it that is theoretically equal. However, once they begin the job, the relationship changes form and begins to be more and more hierarchical. The worker is expected to do what the boss says and the boss is not expected to do what the worker says. The equal, or, at least, supposedly equal, exchange no longer happens except on pay day. As the relation becomes hierarchical, the reciprocity becomes an afterthought rather than the basis of the relationship.

And the state is an entity of hierarchical relations. Things flow from the citizens to the government officials and the police. If there is hierarchy, then communism hasn't been fully universalized as those relations which are based upon hierarchy are not based upon communism.

Now, you'll notice that the two biggest forms of anarchism are based upon the two non-hierarchical forms of relations. Anarcho-communism is the universalization of, well, communism and mutualism is the universalization of reciprocity. When Proudhon spoke of the anarchic encounter, he was, I believe, essentially outlining the theoretical ideal of reciprocity. Two individuals meet as equals, and, as equals, they exchange equally. That is the heart of reciprocity and that is what Proudhon's system was built upon. Communists, on the other hand, tend to conceive of things as "gifts" rather than as exchanges and imagine an economy where everything is given as a gift rather than as an exchange. That is what the communistic system is built upon. Both of these, though, lie in a rejection of hierarchy.

Now, while I certainly am a communist and identify as such, I don't think a truly communistic society is possible. While I think we would be able to almost completely eradicate hierarchy, there will be cases in which people are not comfortable or not able to have things flow as communism, be it because they don't know each other or because neither has too little of something as is required for communistic relations to work, so, in those cases, things will flow as reciprocity. Similarly, I don't think a truly reciprocitous society is possible. While, again, the elimination of hierarchy is certainly possible, there will be some cases in which communism will result, such as between lovers or on holidays for gift giving or through debt jubilees. In reality, an anarchist society will always fall somewhere between total communism, which is the ideal of anarcho-communists, duh, and total reciprocity, which is the ideal of mutualists.
However, both reciprocity universalized and communism universalized are fundamentally incompatible with the state and capitalism and any form of hierarchy because the way things flow in hierarchy is antithetical to both. In hierarchy, things flow from those who don't have much to those who have a lot, while in communism it is the opposite as things flow from those who have a lot to those who don't have much. In hierarchy, things flowing up are greater than things flowing down, good apples up, bad apples down, while in reciprocity, things flowing one way are equal to things flowing the other way. The state is based upon hierarchy, so a mutualistic or communistic society is, therefore, incompatible with it.

This is mainly based upon David Graeber's wonderful book Debt: The First Five Thousand Years. Y'all should read it, natch.