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This paper provides an empirical test of the claim that the U.S. Court of Appeals for the Ninth Circuit has too many judges to be able to do a good job. Reversals (especially summary reversals) by the Supreme Court and citations are used as proxies for quality of judicial output. The overall conclusion is that (1) adding judgeships tends to reduce the quality of a court's output and (2) the Ninth Circuit's uniquely high rate of being summarily reversed by the Supreme Court (a) is probably not a statistical fluke and (b) may not be a product simply of that circuit's large number of judges.
Richard A. Posner (Thu,) studied this question.