It's no coincidence that much of the official architecture is based on the Parthenon, which was the Temple of Athena. Democracy was born in Athens. The white columns and triangular pediment above them are the specific features borrowed from that building.
Athenian democracy was pretty weird.
Everyone got a vote, so long as they were male, born not only of parents who were Athenian citizens (maybe one of them -- dunno) but also born in Attica, not a slave, and able to spare the time to attend the assembly rather than make a living, either in Athens or on your farm.
And there wasn't really much of a state apparatus, either -- if someone wanted the city to build a temple, or annex another city state, or declare war on Sparta or Persia, then if he could get the assembly to support him, they'd tell him, OK, go off and organise it and raise an army and equip it, or find some builders or whatever it is.