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Conventional arguments identify either the median justice or the opinion author as the most influential justices in shaping the content of Supreme Court opinions. We develop a model of judicial decision making that suggests that opinions are likely to reflect the views of the median justice in the majority coalition. This result derives from two features of judicial decision making that have received little attention in previous models. The first is that in deciding a case, justices must resolve a concrete dispute, and that they may have preferences over which party wins the specific case confronting them. The second is that justices who are dissatisfied with an opinion are free to write concurrences (and dissents). We demonstrate that both features undermine the bargaining power of the Court's median and shift influence towards the coalition median. An empirical analysis of concurrence behavior provides significant support for the model.