Allahpundit has the roundup of all deep thoughts on the matter. It wouldn't surprise me if she were. I'm pretty sure I was a socialist on or about Oct. 17, 1982, but I was a sophomore in college and probably drunk at the time. My friend and frequent commenter Rich can likely confirm this, although he was probably drunk, too. . . .
I was taking a course called "Sociology and the Law" at the time and my sociology professor, who was influencing my thinking, almost certainly was a socialist, too. There's a lot of that sort of thinking going on in academe and it's hardly news. What's different is that the West Wing has more than a little bit of the typical faculty lounge mentality in it these days. We elected these people, so we just have to deal with it.
So that leaves the question: is Elena Kagan a socialist now? Based on the available evidence, not likely. We won't find out from reading her old college papers, though.