It's not exactly a rigorous statistical analysis or anything, but Cass Sunstein finds an intriguing pattern in the federal courts of appeals:

A few years ago, I asked a research assistant of mine who had nothing to do that week to look at some environmental cases to see how Republican appointees vote, depending on whether they are sitting with two Republican appointees or at least one Democratic appointee. If we construct something like Colorado Springs, Bush country, on the federal judiciary, just by looking at RRR panels, how do RRR panels look in environmental cases compared to how they look when it's mixed?

She collected about 40 or 50 votes. We didn't have enough to do statistical tests, but we did have enough to be startled, to find that Rs, Republican appointees, show very conservative voting patterns on the federal courts when they are sitting with two other Rs. In a case in which the Sierra Club or the Natural Resources Defense Council is suing the EPA [Environmental Protection Agency] to get it to do more, Rs on our panels vote for them about 20 percent of the time. Rs are much more likely to vote for them—environmental groups—when there is at least one D present. The divergence is very dramatic.

This makes plenty of intuitive sense—putting just one Democratic appointee on a panel would likely make the other judges just a wee bit more liberal (or at least prevent a panel of all Republicans from becoming even more conservative in their views through the echo chamber effect), and vice versa. Except then this train goes off the rails: Sunstein later says this pattern doesn't hold for the Sixth Circuit court of appeals. His explanation: "[O]n the Sixth Circuit, the Democratic appointees and Republican appointees hate each other. They don't listen." But why on earth would that be the case?