In the case of Liljeberg v. Health Services Acquisition Corp., the U.S. Supreme Court ruled that a federal judge should have recused himself from presiding over a lawsuit because he was on the board of trustees for one party involved in the litigation, Loyola University. The university had an indirect interest in this case as it could potentially benefit from its outcome due to its relationship with one of the litigants, Health Services Acquisition Corporation (HSAC). Despite not having direct financial interests or involvement in decision-making related to HSAC's operations at Loyola, his role created an appearance of partiality which violated Section 455(a) of Federal Judiciary Law requiring judges' disqualification if their impartiality might reasonably be questioned. This ruling established that even potential conflicts can undermine public confidence and must be avoided to maintain integrity within judicial proceedings.

In the dissenting opinion for Liljeberg v. Health Services Acquisition Corp., Justice Scalia argued that the majority's decision to vacate and remand was based on a misinterpretation of 28 U.S.C. §455, which requires judges to recuse themselves in any proceeding where their impartiality might reasonably be questioned. He contended that this statute should not apply retroactively, meaning it shouldn't invalidate decisions made prior to a judge realizing they had a conflict of interest or bias relevant to the case at hand. In his view, applying this rule retrospectively would create an impractical standard and could potentially undermine public confidence in judicial proceedings by suggesting that many past judgments were biased or unfair due to undisclosed conflicts of interest from presiding judges.