In existing models of direct democratic institutions, the median voter benefits, but representative politicians are harmed since their policy choices can be overridden. This is a puzzle, since representative politicians were instrumental in creating these institutions. I build a model of direct democracy that explains why a representative might benefit from tying his or her own hands in this way. The key features are (1) that voters are uncertain about their representative's preferences; (2) that direct and representative elections are complementary ways for voters to control outcomes. The model shows that some politicians benefit from the introduction of direct democracy, since they are more likely to survive representative elections: direct democracy credibly prevents politicians from realising extreme outcomes. Historical evidence from the introduction of the initiative, referendum and recall in America broadly supports the theory, which also explains two empirical results that have puzzled scholars: legislators are trusted less, but reelected more, in US states with direct democracy. I conclude by discussing the potential for incomplete information and signaling models to improve our understanding of institutional change more generally.