Wikipedia defines “hierarchy” as: “an arrangement of items that are represented as being above, below or at the same level as one another.” For many people, the word itself (and the implied notions of superiority and inferiority) have a negative connotation. In this essay we use the term in a neutral sense, as a practical way for a system observer to think about hierarchical structures and relationships between the different elements in the system. We’ll take a look at where hierarchy comes from in the first place, beginning with complex systems consisting of non-adaptive components. From that we’ll derive the characteristics of hierarchy and what hierarchy does to the system once it’s in place. Finally we’ll carry those concepts over to complex adaptive systems.
Let’s start by looking at a regular complex system. As an example, consider a bunch of carbon, oxygen and nitrogen atoms. These particles have no consciousness or free will, but they can interact with each other in chemical reactions producing organic molecules. These organic molecules in turn also interact, forming new structures such as amino acids, proteins, and so on in higher order structures. We quite naturally think of this in terms of “higher order structures” because some system elements are building blocks for other systems elements. Atoms are the building blocks and molecules and amino acids are the building blocks of proteins, not the other way around. Such a structure is basically what we mean we when use the word “hierarchy”. It is not necessary to assign any value or moral judgment to this relationship.
The system observer always chooses how to see and model the system under analysis, and will construct this model in function of the research questions. The model of a theoretical, average human being will be very different, for example, depending on whether we’re interested in economic decision making or physical performance in an endurance sports event. There is no obligation for a system observer to think in terms of hierarchy, but it often the most efficient way to describe phenomena at different levels. The earth’s atmosphere consists of a bunch of oxygen and nitrogen molecules, but at some point it begins to make more sense for an observer to think in terms of “wind” or “tornado models” as higher order structures for the purpose of weather related questions. It would be quite tedious to keep describing these phenomena in terms of molecules (or, for that matter: electrons and protons or more elementary particles…) When you hear about emergence in complex systems, this is what people mean: interaction at lower levels leading to (sometimes spectacularly different) phenomena at a higher level.
The “building block” relation has an opposite, giving us another useful analytical concept: the higher order element in some way reduces the degrees of freedom of the lower order elements. An atom can’t easily bind with another one if it is already part of an existing molecule. The higher order structure is an important part of the system context for some element. What happens next to a carbon atom will be very different depending on whether it is part of a diamond crystal or of a methane molecule about to be burnt. Again this restriction is just a neutral fact, but observers often express bias embedded in the choice of words used to describe this effect. When the system observer or analyst views the effect as positive, the higher order level might be described as “stabilizing” the lower level, for example. For undesirable effects, you might see words like “constraining” or “restricting”. (Admittedly such language creeps in more often in adaptive systems and especially those in the realm of social sciences… In vanilla complex systems such as electronic networks it is less of a problem. The interesting borderline case is environmental ecosystems, where phenomena are literally natural but observations often infused with human qualities.)
A third differentiating characteristic between different hierarchical levels in a system is the pace of change. Higher levels have slower process speeds and change cycles than lower levels. Tree leaves and flowers function on an annual cycle, branches and trunks and the tree itself on a timespan of decades, and a forest of trees over centuries. For non-adaptive systems this is quite obvious and simply a “baked in” result of the emergence process. If higher levels decayed or collapsed faster than lower levels, they wouldn’t be around long enough to be considered as a separate system element. If a higher level is stable, it has to be slower than its lower levels. This is less obvious for adaptive systems, which we’ll look at next..
In a complex adaptive system, individual elements have some form of decision making process, allowing them to change the strategy determining their behavior and actions in the system. But as a system observer, we can still use the same criteria characterizing hierarchy in an ordinary complex system. Can we differentiate subsystems that are best described using different models? Do we see system elements influencing the degrees of freedom other elements, be it stabilizing or constraining? Can we spot different processes operating on different timelines? And when all of this is going on in our system, doesn’t that mean we can see order and structure between the different parts of the system – a hierarchy, in other words?
Framed through these lenses, the United States Congress (for example) has a hierarchical governance relationship with individual US citizens in the context of a social system. Factually, Congress is no more than a group of 535 citizens. But within the US society system this group obviously doesn’t function like any other random collection of 535 citizens. A useful description of “Congress” as a separate element in the political system contains specific and different terminology than the language used to describe citizens. “The United States Congress is the legislature of the federal government of the United States. It is bicameral, being composed of a lower body, the House of Representatives, and an upper body, the Senate.”, to quote the first two sentences of the Wikipedia entry. As a hierarchical element, Congress didn’t spontaneously emerge as a consequence of interactions between US citizens. It was designed, and it could have been designed differently. But designed or natural, all the characteristics of a hierarchy are present. Congress reduces the degrees of freedom of individual citizens through legislation. It is described in completely different language and concepts than those applicable to individual citizens. And it operates on a timescale far exceeding the lifespan of even the oldest of individual congress members.
Emerged and designed hierarchies operate in a similar way, but there is an important difference. Complex adaptive systems can have both types. Individual human beings driving around in cars are definitely agents with the capability to take decisions and alter their behavior, but the traffic created by their interactions is emergent, not designed. It is a different hierarchical level as we describe it in different concepts (such as “traffic jam”), it’s of a higher order because individual drivers are the “building blocks” it has a constraining effect on, and it operates over a longer timeframe since traffic persists while individual drivers continuously start and stop participating. The difference between emerged and designed hierarchies in a CAS is based on the kind of information used in the agents’ decision engine. If the agent only uses its own local observations, the system isn’t all that different from any other populated by elements following pre-programed rules, and hierarchy will be emergent. In designed hierarchies, on the other hand, agents also incorporate information from other levels in the system as input and use it to deliberately create hierarchy.
It is not difficult to find examples in politics, economics or other areas of the human enterprise. Notions of the common good resulted in the formation of clans, institutions and nation states (and nation states went on to create other levels, such as mutual defense treaties and other international bodies). The division between natural emergence and deliberate design is not always a hard one, but is also not very important. A phenomenon like clan formation is so universal that it seems more like a naturally emerging process as opposed to a deliberate act by rational minds. Once created though, the higher level in a designed hierarchy will take on a life of its own and exercise constraining effects over lower levels – even if those were its original creators. In this they aren’t very different than emerging hierarchies.
As mentioned in the introduction of this essay, we make no value judgments about the fairness or desirability of hierarchical structures in some system. Hierarchical levels are anyway not real things, just conceptual constructs in the mind of the observer to facilitate description and analysis of specific research questions. But all hierarchies universally operate the same way in every system. Stewart Brand captures it beautifully in his essay “Pace layering: how complex systems learn and keep learning”:
“From the fastest layers to the slowest layers in the system, the relationship can be described as follows:
Fast learns, slow remembers. Fast proposes, slow disposes. Fast is discontinuous, slow is continuous. Fast and small instructs slow and big by accrued innovation and by occasional revolution. Slow and big controls small and fast by constraint and constancy. Fast gets all our attention, slow has all the power.
All durable dynamic systems have this sort of structure. It is what makes them adaptable and robust.”
 As a reminder, we use the term “adaptive” when the elements in a system have some capability to take decisions, follow and change their strategies or otherwise alter their behavior. A sandpile can be studied as a complex system, but the grains of sand have no capability to change their behavior. Contrast this with car drivers, who can take decisions and adapt in response to what happens in their environment: as a result “traffic” is an example of a complex adaptive system.