No. Not unless, broadly speaking, that U.S. Supreme Court justice could determine that s/he had conflict(s) of interest or an appearance of conflict(s) that would render his/her decision to be biased, prejudicial, or otherwise derive an unfair judicial review/outcome of the issues of the litigating parties. (See, for example,
28 U.S. 455 . . .
and . . .
http://www.uscourts.gov/guide/vol2/ch1.html . . . but see footnote 3)
(footnote #) 3. This Code governs the conduct of United States Circuit Judges, District Judges, Court of International Trade Judges, Court of Federal Claims Judges, Bankruptcy Judges, and Magistrate Judges. In addition, certain provisions of this Code apply to special masters and commissioners as indicated in the "Compliance" section."
http://www.uscourts.gov/guide/vol2/ch1.html
However, that being said whether statutory federal law or judicial ethical code, the determining factor of these decisions rests with each U.S. Supreme Court justice. There is no higher determination as an overview:
(Former Chief Justice) Rehnquist offered no conclusions about the issue, but said Scalia alone had the power to recuse himself, at his discretion. "It has long been settled that each justice must decide such a question for himself," he said, although he added that justices often consult among themselves when such issues are raised.
All of which gives rise to questions as to:
(1.) why Justice Scalia's son as an attorney for the same law firm that represented Bush while before the SCOTUS in
Bush v. Gore but Scalia didn't recuse himself. That same Scalia kid -- Eugene Scalia -- became head attorney for the Department of Labor under George Walker Bush. Did Justice Scalia have an interest in the outcome of
Bush v. Gore?
(2.)
Justice Thomas' wife worked for the Heritage Foundation that had interests in
Bush v. Gore but Thomas didn't recuse himself. Did Justice Thomas have an interest in the outcome of
Bush v. Gore?
(3.) Chief Justice William H. Rehnquist, whose lawyer son worked for the law firm representing Microsoft against private antitrust lawsuits, participated in a key U.S. Supreme Court vote in a Microsoft antitrust case. Rehnquist explained in a separate U.S. Supreme Court "note" writing that he had reviewed the law and concluded there was no conflict of interest. Did Justice Rehnquist have an interest in the outcome of that Microsoft case? Was there an appearance of impropriety?
(4.) And, most of America knows of Justice Scalia's duck hunting trip with Vice President Dick Cheney and Cheney's son in which he shared both airplane facilities as well as housing accommodations but Scalia didn't recuse himself. Did Justice Scalia have an interest in the outcome of that Cheney case? Was he influenced by the gratuities from Cheney and company? Was there an appearance of impropriety?
Justice Breyer, on the other hand, is well-known to recuse himself as are Justices Ginsburg and Stephens.
BTW, of the five Roman Catholic Church majority members of this present (Roberts Court) U.S. Supreme Court bench, four of whom are known to be (rightwing) ultra-conservatives: Justice Antonin Scalia, Justice Clarence Thomas, Chief Justice John Roberts, and Justice Samuel Alito. The remaining fifth justice of the majority is Justice Anthony Kennedy, a moderate-to-conservative but he can swing ultra-conservative at times too. Again, will these justices recuse themselves if they have a conflict of interest? Or will they, too, oft-handedly openly say from the SCOTUS bench during oral arguments:
"I bet that 90% of the American people believe in the 10 Commandments and 85% don't know what they all are; they (the 10 Commandments) are a symbol that this government derives its authority from God and that seems to me entirely appropriate." - Justice Antonin Scalia, March 2, 2005, speaking from the bench of the U.S. Supreme Court during oral arguments demonstrating his inability to Separate Church and State from his own religious beliefs.
.