Though openness in government has obvious benefits, recent scholarship has devoted less attention to the possibility that it might also have costs. I use a formal framework to investigate the effect of public versus private decision making on opinion polarization. Existing work emphasizes that public debate helps to reduce polarization and promote consensus, but I argue that when debate takes place between representatives the opposite may be true. When representatives make decisions in public, they face incentives to use their actions as a signal of loyalty to their constituents, potentially ignoring private information about the true desirability of different policies. Anticipating this, constituents will not alter their prior policy beliefs following a debate of this type. When representatives instead make policy decisions in private, they are more likely to allow private information to influence their actions. An important consequence is that even if constituents do not observe actions or statements of individual representatives, they can still use the final policy choice to revise their initial beliefs. I suggest that these conclusions have significant implications for both the literature on deliberative democracy and for discussions of polarization in American politics.