The central question of the system of government

Hello, we have all seen the videos on the constitutions of Athens, Sparta, Rome, and England (to some extent). I would like to tell you a little story so you guys will get the question I am asking.

For the entire history of mankind, people have understood that when you push on an object, it moves from its place. These concepts: push, move, and place had been used long before we had an exact description of what they mean. For example, as far as I can find on the internet, the exact definition of speed (change in position over a small time step) was not explicitly laid out until the 14th century.

Today, people know in the same way ancient peoples knew about speed in intuitive terms what goals and what definitions our modern system of government uses. I ask you, dear reader, to state your goals of government and the exact definitions and assumptions you use to create a system to fulfill that goal.