How did Athens and Rome develop new ideas about the role of
citizens in their government?

Athens developed a form or direct democracy, perhaps the oldest democracy in the world. In this democracy, a few citizens, mainly land-owning men, met in a central place: the agora, to discuss important matters about the city and take political decisions.

Rome developed the Republican form of government. The two main social classes of Roman society, the Plebeians and the Patricians, send representatives to the Roman deliverative body: the Senate, where the main discussions and political decisions were taken.

if you are talking about current time the answer is no

if you are talking about when the colonies were developing the answer is yes

the virginia plan called for three branches of government and two houses of congress. representation in each house would be determined by population. the new jersey plan called for three branches of government and a single house of congress. each state would have an equal vote.