There are concerns amongst researchers and the general public that social media platforms threaten democratic values. Social media corporations and their engineers have responded to these concerns with various design solutions. Though the objective of designing social media democratically sounds straightforward, the concrete reality is not. The authors discuss what a democratic design for social media platforms could look like by exploring two classical conceptions of democracy, one in the liberal tradition and the other in the deliberative tradition. In particular, they discuss three concerns: 1) mis- and disinformation; 2) hate speech; and 3) the relations between filter bubbles, echo chambers, and public debate. By describing the underlying ideals of the two traditions and translating these into design guidelines, the authors make explicit how varied and contrary the implications of different conceptions of democracy can be for addressing public concerns and designing for democratic social media. With these things in mind, this article responds to a call, which is to raise awareness among social media corporations, engineers, and policymakers about varying democratic ideals and the implications that these may have for social media.