Waltz claimed that although functional differentiation is inherently a feature of the structure of political systems, the units of anarchic systems are functionally undifferentiated. But states clearly perform differentiation functions than nonstate actors. And, as Waltz emphasized, great powers perform managerial functions in international systems that lesser powers do not. Furthermore, his focus on the similarity of great powers ignores this functional differentiation in the system in favor of attention to particular attributes of one type of parts. Turning to the distribution of capabilities, Waltz’s focus on system polarity (the number of great powers) looks not at how capabilities are actually distributed but only where they are concentrated. This is especially unfortunate because the relativity of power means that the places where capabilities are not concentrated is of great structural importance. And Waltz perversely excludes inequalities of power and relations between the strong and the weak from his account of international political structures.

One of Waltz’s major contributions was the idea that political structures can be specified, in a rough first approximation, by ordering principle, functional differentiation, and distribution of capabilities – an understanding that remains largely taken-for-granted in contemporary IR. This chapter shows, however, that this tripartite conception can neither accurately nor fruitfully depict the structure of three simple anarchic systems: the Hobbesian state of nature, immediate-return forager societies, and great power states systems. In fact, Waltz’s depiction of great power states systems, his implicit model of a generic international system, is wildly inaccurate on all three of his dimensions of structure. Great power states systems, rather than lack hierarchy, are structured by the hierarchical superiority of states and great powers. Great powers, states, and nonstate actors perform different political functions. And the standard Waltzian account of the distribution of capabilities as a matter of the number of great powers (“polarity”) is about as useful as depicting the distribution of wealth in a society by the number of billionaires.