As you've learned from Stambaugh and the lectures in class, Rome was a strange kind of democracy, with voting in both of its major assemblies skewed in favor of the rich. However, during the Republic the votes of the lower classes still mattered, especially in the "Comitia Tributa." In the empire, the emperor was charged with balancing the concerns of the elite and the poor...if he didn't, he might be assassinated, or the city might erupt in riots.
Click HERE for an overview of Roman politics.