We study the ability of a social media platform with a political agenda to influence voting outcomes. Our benchmark is Condorcet's jury theorem, which states that the likelihood of a correct decision under majority voting increases with the number of voters. We show how information manipulation by a social media platform can overturn the jury theorem, thereby undermining democracy. We also show that sometimes the platform can do so only by providing information that is biased in the opposite direction of its preferred outcome. Finally, we compare manipulation of voting outcomes through social media to manipulation through traditional media.