The National Law Journal has a nice explanation of the pending Supreme Court case on judicial recusal here. In essence, a West Virginia Supreme Court justice refused to recuse himself from a case in which a corporate litigant's president had previously donated $3 million dollars to the judge's judicial campaign. The issue is whether the judge's failure to recuse himself violated the due process clause.
NYU's Stephen Gillers is quoted in the article and has it exactly right. Here's the relevant excerpt:
That seems to cut to the core of it. I don't care whether the West Virginia judge thought that he could be unbiased. Personally, I don't think that such a belief would have been reasonable, unless the judge had the objectivity of Ronald Dworkin's Hercules. But even if the judge had such herculean objectivity, the appearance of bias is so strong here that the judge's failure to recuse himself has to violate our sense of procedural fairness. As Professor Gillers suggests, all you have to do is ask yourself whether a litigation outcome would seem fair to you if your adversary contributed $3 million to the judge who was presiding over your case.
Even though this case seems fairly clear, the challenge for the Court is to come up with a due process test that can be applied in future cases. The easiest solution is the one that Monroe Freedman mentioned in his comment to this post: rule that judicial elections themselves are a violation of due process. I don't expect the Supreme Court to buy that argument, but there's a lot to be said for that position.