The only thing more extensive than the number of people who work for or are contracted by the government are the number of things which are touched by public policy (= a rule with the force of law made by a legitimate policy maker). Look around you - you are surrounded by public policy. Your electricity is probably provided by the city, the rates you pay for telephone service are regulated, the freon in your air conditioner and refrigerator are regulated, the quality of the air you breath and water you drink is regulated, what is broadcast over the public airwaves (TV,radio) is regulated, what you can and can't have in your medicine cabinet is regulated, the ownership of the software you are using is regulated, the amount of radiation and interference caused by everything electrical in your house is regulated...
Okay, that's enough...you should be getting the impression now that a political system is much more than just those people in the capitol who get on the TV and in the newspapers and scream at each other. The political system touches everyone, sometimes in very personal ways.
A political system is EVERYTHING involved in the "authoritative allocation of values and resources" (includes both tangible and intangible values and resources) in a society. Or, it is everything involved in the creation and implementation of public policy. It includes the citizens of that political system, all government workers and representatives, structures, and processes. It includes the Constitution (written or traditional) and any other informal "rules of the game". Systems can be broken into subsystems...a component of a political system that is a system in its own right. For example, the "US political system" has among its subsystems, the individual states.
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