Here's the definition of "extraordinary situation that Constitutionally-requires recusal":
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The (supported) premise "thou shalt not ever show clear/probable bias" from Caperton v Massey Coal 2009:
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.
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Ginsburg and Kagan stumping as activists for gay marriage nationwide, and performing gay marriages in their spare time while the question was pending "should the states be able to deny gays marrying" yet to be Heard, REQUIRED MANDATORY RECUSAL clearly, and inarguably according to Ginsburg and Kagan's own Standard they themselves voted "aye" on in the 2009 Caperton v Massey Coal premise/conclusion.
In so stumping and being activists and performing gay marriages while the question was pending (a thing they absolutely must not have done according to the requirements of their office and position...but did anyway), they showed clear and undeniable evidence to the world that their minds were already made up before they entered the Courtroom last Spring. And so doing, they met the "extraordinary Constitutionally-requirement to recuse themselves". There could be no person on earth viewing either of these Justices doing what they did and saying what they said publicly prior to the Hearing that would have even a subatomic particle of doubt that Kagan and Ginsburg already were going to vote against states being able to say "no" to gay marriage.