Matias Iaryczower and Matthew Shum have posted this draft on SSRN:

We study how campaign contributions affect the voting strategies and effectiveness of justices in the Supreme Court of eight US states. A judge’s voting strategy leans more heavily towards an interest group the larger are its contributions to the judge, and the smaller are its contributions to other members of the court. This indirect effect is consistent with an equilibrium adjustment to contributions to other members of the court. Observed contributions have a large effect on the behavior of individual judges — affecting both the probability that they vote to overturn a decision of the lower court and the probability that they support an incorrect decision — but they have a small effect on the decisions and effectiveness of the Court.

I look forward to reading this piece.  If the research bears out, this is potentially very important.