Final answer:
The modern democratic principle influenced by ancient Greek and Roman ideas is civic responsibility, where citizens feel responsible for participating in government.
Step-by-step explanation:
The modern democratic principle that was influenced by ancient Greek and Roman ideas of citizen participation in government is civic responsibility.
In ancient Greece, the concept of democracy was developed in the city-state of Athens, where citizens directly voted on laws and government matters. This idea of direct democracy influenced the Roman Republic, which introduced the concept of representative democracy, where citizens elected representatives to act on their behalf.
In modern times, citizens' civic responsibility to participate in government has been emphasized as an important principle in democratic societies, including the United States. This means that all citizens should feel a sense of responsibility to engage in the political process, such as voting, staying informed about current events, and actively participating in their communities.