The concept of social hierarchy is almost inseparable from the sort of large-scale organization that became possible with the origin of the state. In the modern world, most of us participate at least two organizational hierarchies (our state and our employer), and often more. While many seem to feel that hierarchy is undesirable because it causes individual oppression and organizational inflexibility, and while newer communication technologies and increased reliance on a specialized market of services (Outsourcing) may make flatter and more fluid organizations possible, we think that some degree of hierarchy is necessary for coordinating most large-scale activities. Although hierarchies are socially constructed in rather arbitrary ways, there are nonetheless good reasons why societies have constructed hierarchies.

Our basic argument is that there are inherent semantic benefits of hierarchical organization that explain the prevalence of this pattern.

It is generally agreed that a fundamental aspect of social hierarchy is a clear understanding about who must obey whom—a formal power relation, as in the military Chain of command. The related mathematical concept is the partial ordering. Formally, this says is that the can-boss relation is a Transitive relation, like numerical >=. If Joe can-boss Fred, and Fred can-boss Bill, then Joe can-boss Bill. In addition, aside from the fact that everyone can-boss themselves, nobody that we can boss can also boss us (A can-boss B implies B cannot-boss A.)

An important subtlety of this is in the term partial ordering. There may be people A and B such that neither A can-boss B nor B can-boss A, and in fact this is true for most pairs of individuals in an organizational hierarchy.

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For example, neither Kelly can-boss Carl nor Carl can-boss Kelly.

Usually organizational hierarchy has an additional property not required by the mathematical definition of partial ordering: everyone has exactly one immediate boss, except for a single top boss. Mathematically this says that the organizational chart is a tree. This relates to the vital organizational function of the hierarchy, which is to provide a Decision procedure in any case where it is unclear how to proceed according to standard procedures: “We'd better ask the boss.”

In organizational hierarchies it is not true that information is constrained to flow only in the hierarchy. For example, Ed can send a purchasing order to Betty, even though there is no hierarchical relation between them (and Betty might seem to outrank him.) Purchasing is Standard operating procedure, and functions in parallel to the hierarchy.

To see the importance of the partial ordering aspect of hierarchy, consider what would happen if Carl came into Kelly's office shouting demands. She might be pretty nervous, but likely she'd clear it with Larry before doing anything. Though Carl is head of purchasing, he cannot-boss Kelly. In the military organization this is clearer as the distinction between rank and the Chain of command.

Formal rank is found mainly inside organizational hierarchies, and is ordinarily subordinated to it. Rank is a simpler, more impoverished concept that is usefully unsubtle at times. When possible, the military functions through its organizational hierarchy (the chain of command), but rank is also well-defined, and in urgent situations where kicking the decision up the chain of command is not reasonable, soldiers are taught to obey anyone with a higher rank.

“hierarchy” is often used to mean any formal system for determining can-boss. The rank system does define a partial ordering, and it has the usefully different property of more closely approximating a Total order. Rank defines the can-boss relation between many more pairs of individuals (any two who differ in rank.) These two hierarchies coexist in the military, and are made compatible by insuring that rank increases as you go up the chain of command. Even in organizations that lack formal rank there may be some sense of unease with having a boss who seems in some way inferior (such as being younger or having lower seniority.)

Note that the Wikipedia Military rank article is itself rather loose about the relationship between rank and hierarchy:

Military rank is a system of hierarchical relationships in armed forces or civil institutions organized along military lines.

This confusion between rank hierarchy and organizational hierarchy is long-standing, and the association of rank with violent oppression and animal dominance leads many to think that hierarchy is bad, and that we should strive to move beyond it. But this ignores the tremendous power of the uniquely human organizational hierarchy to coordinate large-scale cooperative behavior.

A rank hierarchy much more closely matches the concept of an animal Dominance hierarchy than does the partially ordered organizational hierarchy, and this rooting in our ancestry as social animals explains our emotional reaction to rank differences. Although an organizational hierarchy may lack a formal rank system, as social animals we are highly aware of dominance relations, and people gauge their dominance by how high they are in the hierarchy, both in terms of how many levels they are away from the boss, and by how many people they command.

Dominance is an ancient system which gene/culture Genetic-Cultural Coevolution has seized upon as a mechanism to enable the the creation of the much more powerful organizational hierarchy.

While many have noticed the uncanny similarity of chimpanzee politics to human political maneuvering, this superficial similarity conceals a profound difference. Dominance isn't organizational hierarchy, and it isn't even rank. In a real organization, asserting control is not always as simple as issuing a command, but when a boss is displeased by the organizational response and talks about “bashing heads all the way down the line”, he is speaking figuratively. For chimpanzees, the alpha male can do pretty much whatever he wants, but getting any other individual to obey still rests closely on the threat of violence, and other than leading by example, commanding any coordinated action is beyond his power.

An important aspect of the partial ordering in hierarchy is that the ambiguity of individuals with no can-boss relation (such as Betty and Ed) relates to the economic phenomenon of Division of labour and the conceptual principle of Modularity. These are inextricably tied to the practice of organizational hierarchy, and are the primary reason that hierarchy adds value beyond that achieved by mere rank. Betty and Ed don't need any can-boss relationship because they perform distinct functions in the division of labor. The company has been divided into sub-organizations with distinct functions, and although the organizations do interact in non-hierarchical ways (such as by purchase orders), these interfaces are clearly defined to insure modularity. So, even though Ed may know Betty ordinarily handles purchase orders, he doesn't just call her up and say what he needs. Instead, he fills out a form and sends it to “the purchasing department.” If Betty happens to be on vacation, it's Carl's job to make sure that the P.O. still gets handled somehow, and Ed doesn't even need to know.

See also: Hierarchy and Hierarchical organization