Elected officials are commonly accused of being ideologically rigid, or failing to alter their positions in response to relevant policy information. We examine this phenomenon with a theory in which politicians have private information about their ideological leanings and expected policy consequences. The theory shows that in many circumstances the informational differences create a context in which elections induce ideological rigidity. Correspondingly, elections often fail to provide incentives for information-based moderation, in which both left- and right-leaning politicians become more likely to use policy information. These seemingly perverse incentives occur because politicians wish to signal that they share voters' leanings; indeed, the motivation to signal preference similarity can induce rigidity even when voters want politicians to be responsive to new information. We show that such incentives for rigidity are greater when voters have less information about policy and politicians' preferences, and discuss possible tests of these predictions.