In "Bargaining and Strategic Voting on Appellate Courts" Chuck Cameron studies how appellate courts and regulatory commissions produce case dispositions and rules rationalizing the dispositions. He shows that the median judge is pivotal over case dispositions, although she and others may not vote sincerely. Strategic dispositional voting is more likely when the case location is extreme, resulting in majority coalitions that give the appearance of less polarization on the court than is the case. The equilibrium policy created in the majority opinion generically does not coincide with the ideal policy of the median judge in either the dispositional majority or the bench as a whole. Rather, opinions approach a weighted center of the dispositional majority but often reflect the preferences of the opinion author. 

Parameswaran, Giri, Charles M. Cameron, and Lewis A. Kornhauser. "Bargaining and strategic voting on Appellate Courts." American Political Science Review (2019): 1-16.