The rise in popularity of Twitter has led to a debate on its impact on public opinions. The optimists foresee an increase in online participation and democratization due to social media's personal and interactive nature. Cyber-pessimists, on the other hand, explain how social media can lead to selective exposure and can be used as a disguise for those in power to disseminate biased information. To investigate this debate empirically, we evaluate Twitter as a public sphere using four metrics: equality, diversity, reciprocity and quality. Using these measurements, we analyze the communication patterns between individuals of different hierarchical levels and ideologies. We do this within the context of three diverse conflicts: Israel-Palestine, US Democrats-Republicans, and FC Barcelona-Real Madrid. In all cases, we collect data around a central pair of Twitter accounts representing the two main parties. Our results show in a quantitative manner that Twitter is not an ideal public sphere for democratic conversations and that hierarchical effects are part of the reason why it is not.