In ancient Greece only male adults, members of the aristocracy had full political, economic and social rights and were allowed to participate in the decision-making process through direct democracy. On the other hand, women, laborers, merchants, children, slaves and foreigners had minimum rights are were not allow to participate in the political process due to their lack of capacity to be independent from someone's protection.
Today, ancient Greek democracy wouldn't be considered a democracy in the terms we understand it. There was a deep social division that didn't allow a large amount of the population to decide about their own fate and to be renegade it as second class citizens.
The most important criteria regarding citizenship lies first of all in the rights and responsibilities of US citizens which are established in the Constitution. Which are there to guarantee people's participation as well as their protection and representation. ("3 different United States, Hooven & Allison vs Evatt).