Now let's add local government, the level of government that doesn't appear in the constitution.

The arrow from state to local government illustrates that local governments are more or less creatures of the state level of government, holding power at the pleasure of the state and devoid of constitutional protection. Later we'll have to discuss whether that's a good thing or a bad.

By convention, though, state governments allow the people to elect their own local government representatives, hence the arrow from the people to local government.