The author identifies five principles underlying Federal disqualification doctrine. These principles provide judges with considerable leeway and reflect the conventional wisdom from which rules are made by Congress and the courts. He then analyzes two theories of judicial disqualification -- political adjudication and cognitive judging -- and finds neither of these theories to be satisfactory. Judicial disqualification under the political adjudication method would politicize the judicial process and result in judicial paralysis. The other method, cognitive judging, is flawed, because it is mechanistic and because no judge can ignore his or her value system. The author proposes a third theory based on the view that adjudication is a form of constrained dialog. From this theory, three principles of judging are derived. First, a judge should not decide a case on personal considerations. Second, a judge should be willing to consider all arguments that are relevant. Third, a judge should not have extrajudicial knowledge of certain relevant facts in the case. One advantage of the constrained dialog theory, it is concluded, is that it recognizes a limited role for disqualification. 266 footnotes.