I've focused occasionally on the idea of "levels" of social arrangements, from the local to the intermediate to the higher levels, with the idea that higher levels are composed of structures and activities at lower levels. Generally I've had in mind examples from one specific area of the social sciences to illustrate these points -- sociology. How do these claims look, however, when we consider them in light of political science?
If we wanted to provide a brief definition of "politics", it might go along these lines: the institutions and patterns of behavior through which decisions about public policies and the expenditure of public resources are determined and implemented. This includes study of the personnel of governing institutions; the nature of governing institutions; and the strategies and behavior of all those affected by those institutions.
There is one clear sense in which politics and government contain "levels". This derives from the fact that governance systems have a hierarchical, semi-nested structure of ascending scope of control and authority. In the United States we have Federal laws, state laws, and county and municipal laws. And this differentiation also imposes a criterion of level: higher level means broader jurisdiction over territory and population. Each possesses a set of legislative institutions and officials, along with a bureaucracy focused on implementation and enforcement. These zones of governance authority differ in terms of scope and scale, with units of governance ranging from national to state to county and city.
However, these zones of political governance are not hierarchical in another important sense: the Federal level is not composed of the state or municipal governance systems. Rather, each is independent from the other. Higher-level units have the authority to enact rules and laws (in some instances) that constrain the actions of the lower-level jurisdictions. But the personnel, officials, and systems of the two jurisdictions are distinct and independent. And it is entirely possible, even predictable, that there will be policy disagreements between them.
A second clear interpretation of "levels" of governance corresponds to the formal hierarchy of a large administrative system. The President exercises authority at the highest level within the executive branch. Cabinet secretaries report to the president and manage and direct complex and extensive organizations (Departments) dedicated to specific functions: Justice, Environmental Protection, Education, ... Each department of the executive branch in turn consists of a descending proliferation of bureaus, regional offices, field offices, and the like. The Chicago field office of the XYZ department reports to a regional director, who takes direction from the Secretary. The layers of the organization of government can be referred to as "levels," differentiated by position within a hierarchical system.
It is also evident that the networks of power and influence that operate at the Federal level are distinct from those at the state or local level. The powerful individuals are different, the organizations through which they exercise their influence are different, and the sources of their power are different. The Daley machine in Chicago in the 1960s exercised great power in city politics, middling power in the corridors of Illinois government, and less influence at the Congressional level. So the different "levels" of government correspond to different loci of influence and activism, and the study of Congressional politics may lead to rather different findings from the study of state or municipal politics.
This means that scholars who are primarily interested in the political mechanisms through which various policies get chosen will select carefully the networks of individuals and organizations they study, in order to shed light on the operative level of governance. But it would be misleading to describe these as different "levels" of politics; rather, different people and organizations are at work in similar policy areas with uncoordinated results in Chicago, Cook County, Springfield, and Washington.
So the idea of "levels" of politics doesn't seem to be a particularly valuable conceptual scheme when it comes to analyzing political behavior and organization. It misleads us into thinking that politics has a fundamental structure from low to high. Instead, we are perhaps better served by a view that picks out various arenas of conflict over resources -- politics -- without the orienting language of higher and lower levels.
Wherever we start our examination of the social world, from the situation of particular individuals, to labor unions, firms, and faith organizations, to federal agencies and multinational trading regimes, the logic of the social world seems to be the same: there are groups of actors planning and acting in that locus, there are structures and rules that surround them, and there are organizations and structures that are broader in scope and jurisdiction and there are such at lesser levels of scope and jurisdiction. There is an up, down, and sideways everywhere in social action. And this is equally true in the zone of political action and institution.