  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.
