Bargaining and Strategic Voting on Appellate Courts

We explore the properties of voting rules and procedures employed by appellate courts in the US. Our model features: (1) a two-stage decision-making process (first over case disposition, then over majority opinion content), (2) dispositional consistency (the new rule must yield the Court's indicated case disposition when applied to the instant case), (3) restricted bargaining entrée (only members of the winning dispositional coalition bargain over policy), (4) competitive offers (potentially many competitive majority opinions), and (5) absolute majority in joins (a majority of the court must endorse the rule in the majority opinion if it is to have precedential power). We show that the median judge is pivotal over case dispositions, although she (and others) may not vote sincerely. Strategic voting becomes more likely as the location of the case becomes more extreme, resulting in majority coalitions that give the appearance of less polarization on the court, than is truly the case. The equilibrium policy depends on the composition of the dispositional majority, and generically does not coincide with the ideal policy of the median judge either in the dispositional majority or the bench as a whole. Rather, opinions are drawn toward a weighted center of the dispositional majority but often reflect the preferences of the opinion author