^^^
Psst - Star Trek was originally created primarily for U.S. audiences, and like it or not 'The Federation' is pretty much modeled after the U.S.A. - just saying.
The Federation has an elected President
A 'Council' that seems to be pretty much like the U.S. Congress
^^^
And I say that because we've never seen them talk about the ability to oust said President with a vote of 'no confidence' so it ain't a British style parliamentary system here. It's always been pretty much "The U.S.A. IN SPAAACE!"