From the work of Christina Boyd, Lee Epstein, and Andrew D. Martin, Boyd and Epstein report:
that we conducted with our colleague Andrew D. Martin, we studied the
votes of federal court of appeals judges in many areas of the law, from
environmental cases to capital punishment and sex discrimination. For
the most part, we found no difference in the voting patterns of male
and female judges, except when it comes to sex discrimination cases.
There, we found that female judges are approximately 10 percent more
likely to rule in favor of the party bringing the discrimination claim.
We also found that the presence of a female judge causes male judges to
vote differently. When male and female judges serve together to decide
a sex discrimination case, the male judges are nearly 15 percent more
likely to rule in favor of the party alleging discrimination than when
they sit with male judges only.
The research paper is here.