Ah a "let's get the thread disappeared flame war". Pretty compelling topic eh guys and gals?
Here are some excerpts from the 2009 Caperton v. A.T. Massey Coal Co. case about when a judge should recuse him/herself. Argument of the premise?.. suspected bias = mandatory recusal:
http://www.supremecourt.gov/oral_arguments/argument_transcripts/08-22.pdf
(page 3 attorney Ted Olsen for petitioners) "
Olsen: "A fair trial in a fair tribunal is a fundamental constitutional right. That means not only the absence of actual bias, but a guarantee against even the probability of an unfair tribunal."
Scalia: "Who says? Have we ever held that?"
Olsen: "You have said that in the Murchison case and in a number of cases, Your Honor....the language of the Murchison case specifically says so. The Court said in that case: "A fair trial in a fair tribunal is a basic requirement of due process. Fairness, of course, requires an absence of actual bias in the trial of cases, but our system of law has always endeavored to prevent even the probability of unfairness." ...(page 4 continues Olsen).."
the Court has said that frequently, not only the probability of bias, the appearance of bias, the likelihood of bias, the inherent suspicion of bias. The Court has repeatedly said that in the context -- a series of contexts or cases...It's probable cause, Mr. Chief Justice (speaking to Roberts now). The Court frequently decides questions involving due process, equal protection, probable cause, speedy trial, on the basis not of mathematical certainty, but in this case
where an objective observer (page 5 continuing) would come to the conclusion -- knowing all of the facts, would come to the conclusion that a judge or jurist would probably be biased against that individual or in favor of his opponent, that would be sufficient under the Due Process Clause, we submit.
Ginsburg:
"Does it mean the same thing as likelihood of bias?"
Olsen: "The Court --
the Court, Justice Ginsburg, has used the changes interchangeably. We think the probably -- the "probable" standard is the one we would advance to this Court. But the -- but
the seminal case, the Tumey case, said that even if there was a possibility -- any procedure where there would be a possible temptation for the judge not to hold the balance nice, clear, and true, would be the standard. But -- and the Aetna --
in the Aetna v. Lavoie case not very many years ago, the Court repeated that standard, and that standard has been repeated again and again.
****************
And so the premise was set to determine that if a judge gave the appearance of bias even, in this case it was campaign contributions, that that judge should have recused himself.
The conclusion of the Court of this case:
Voting 5-4 in a case from West Virginia, the high court said that a judge who remained involved in a lawsuit — one filed against a company helmed by a generous supporter of the justice's campaign — deprived the other side of the constitutional right to a fair trial..."Just as no man is allowed to be a judge in his own cause, similar fears of bias can arise when — without the consent of the other parties — a man chooses the judge in his own cause,"
Court Judges must avoid appearance of bias - politics - Supreme Court NBC News
The men and women invested heavily in getting gay marriage mandated across the 50 states federally instead of seeking permission of the governed for this new social experiment, feel/felt confident to invite Justices during the pendency of the question to preside at their same-sex weddings...and so Justice Ginsburg and then Justice Kagan
actually did!
Thus giving the appearance of bias on behalf of the Court as a whole towards the litigants pushing for federal gay marriage. ").."
the Court has said that frequently, not only the probability of bias, the appearance of bias, the likelihood of bias, the inherent suspicion of bias....
where an objective observer....... knowing all of the facts, would come to the conclusion that a judge or jurist would probably be biased against that individual or in favor of his opponent.."
you are REAAAAAACCHING bro. 
