I Believe their was a Athenian Democracy and they had a constitution. They also had laws and they gave equal rights to the people. They also had franchise's were all men who were birth by both parents. They are enrolled as citizens at the age eighteen.
The people didn't have a say in whether or not they got to run or get elected in office. If you got elected to go into the government, you were pretty much already assigned to that position. The government didn't give the people any say.
Democracy is the rule of the whole the people excluding minors and maniacs only. Whereas Democracy today means government by representatives of the people. It is more democratic by being government by the people instead of government by those elected by the people.
If Athens was a democracy why would they vote people out of the society? Why would they make every one vote on who was the biggest threat to their government system if they were so democratic? While it might be better for the people to be in government, the people who held the real power would have everyone vote someone out to keep their order in Athens.