[F]or every Justice appointed from the October 1986 Term through the October 1993 Term, the newly-appointed Justice voted to grant certiorari less often than his or her predecessor. In fact, the average Justice appointed between 1986 and 1993 voted to grant certiorari 46.2 fewer times per Term than his or her predecessor.
The substitution of Justice Ginsburg for Justice White had the greatest significance. Justice White voted to grant plenary review a prodigious 215.6 times per Term, on average, between 1986 and 1993. Meanwhile, Justice Ginsburg voted to grant plenary review during the October 1993 Term only 63 times, or 29.2% as often as her predecessor.
Usually, we evaluate U.S. Supreme Court justices on a liberal to conservative scale based upon how they vote in cases where certiorari has been granted. But, the invisible votes of Justices on whether to grant certioari or not may have an equally important effect.
The data don't, of course, tell us why new justices granted certiorari less often.
It may, for example, be a product of strategic decision making by Justices when the outcome of a final decision of the court was hard to determine in many cases because the swing voters were unpredictable.
Or, perhaps conservatives have doubts about the desirability of U.S. Surpeme Court review of state courts generally, and trusted increasingly conservative lower federal courts to move jurisprudence in the direction desired with less visibility in most cases, while liberals on the court knew that voting to grant certiorari would often risk have undesired outcomes in an increasingly conservative court.
For the why part of the answer, we will have to wait for memoirs and the release of personal papers.