Jim Highsmith and David Snowden think that self-organization is different from anarchy. They say that self-organization (in a social context) needs some form of management/leadership, and that it otherwise degenerates into anarchy. I disagree.
The origin of the word “anarchy” is: anarchia, from Greek, and from anarchos, which means “having no ruler”. Various dictionaries list two meanings for anarchy:
a) absence of order (or presence of disorder)
b) absence or denial of any authority or established order
In system dynamics, this means either of two things: a) chaos (no order), or b) complexity (order, but not imposed by an authority). This is depicted in the following picture. Governance stretches from order into complexity. And anarchy, the absence of governance, stretches from complexity to chaos.
Anarchy has a bad name, which is undeserved. In the minds of most people, anarchy is equal to chaos. It is a misconception, and probably the main reason why some experts don't like associating self-organization with anarchy. Galaxies behave in an anarchistic manner, and yet they are not chaotic. Ecosystems are anarchistic, but they are also not chaotic. And countries without (working) governments are anarchies, but are also not necessarily chaotic.
A self-organizing system is the complex variant of anarchy. This is true in physics, in chemistry, in biology, and in sociology. There are many definitions of self-organization, and none of them require leadership, management, or authority. In my opinion, it makes no sense to change the meaning of self-organization when applied in a social context.
I think the real issue that some people have with anarchy, is that such unmanaged systems can behave in a way that the stakeholders don't value. When my children are playing a game, running around me and yelling in my ears, I would eagerly agree that this is anarchy. But the children are self-organizing. It just means their way of self-organizing is not very much appreciated by me as their primary stakeholder. And yes, then I prefer to enforce some governance. As Dave Snowden said: “Then you draw a line on the floor, and you tell those kids: if you cross this line, you’re dead.”