In many settings of political bargaining over policy, agents care not only about getting their will but also about having others approve the chosen policy thus giving it more weight. What is the effect on the bargaining outcome when agents care about such legitimacy of the policy? We study this question theoretically and empirically. We show that the median-voter theorem holds in groups that are ideologically very cohesive and in groups with extreme ideological disagreement. However, in groups with intermediate ideological disagreement, the median-voter theorem does not hold. This is since, on the individual level, ideological disagreement with the median has a non-monotonic effect on the policy. We test our model in a natural experimental setting—U.S. appeals courts—where causal identification is based on random assignment of judges into judicial panels, each consisting of three judges who rule on a case. Here judges care about legitimacy of the policy they write because a norm of consensus prevails and because increased legitimacy reduces the likelihood of the judicial case to be heard by the Supreme Court. The predicted pattern of how policies depend on the participants’ ideologies are corroborated by our empirical tests.