Mr. Laser Beam wrote:
They have president which represents all the Federation worlds and not a prime minister.
But Earth's own government appears to be mixed. United Earth is a parliamentary republic - a President as head of state, and a Prime Minister as head of government. This is wholly separate from Federation governmental structure, which has a President as both roles. (Delegates from Federation worlds, Earth included, are Councillors.)
Yeah but there are no politicians. The Federation has its own set of base laws with only some "traditional" and cultural respective planetary laws still in effect.
As far as Earth is concerned in Star Trek. Its a utopian planet where human rights are observed in every corner. People are free to live whatever lifestyle they choose (as long as its legal) and as a result, they've eliminated all major social and economic problems and crime is at a record low (it probably still occurs, but not at the frequency it does in our current time period).