Another chance the Prop 8 team appears to have missed.

Since those days, several published reports have stated that the judge is himself gay. In February, The San Francisco Chronicle called it an “open secret.” Critics have argued that his sexual orientation was a source of bias that should have disqualified him from hearing the Proposition 8 case. Judge Walker has declined to discuss the matter.

Monroe H. Freedman, an expert in legal ethics at Hofstra Law School, said that while bias could lead to recusal in rare cases, “you could say, ‘If a gay judge is disqualified, how about a straight judge?’ There isn’t anybody about whom somebody might say, ‘You’re not truly impartial in this case.’ ”

Mr. Freedman cited a 1975 opinion by Judge Constance Baker Motley of Federal District Court, an African-American jurist who was asked to disqualify herself from a lawsuit alleging unlawful discrimination. “If background or sex or race of each judge were, by definition, sufficient grounds for removal, no judge on this court could hear this case, or many others,” she wrote.

Stephen Gillers, a professor at New York University Law School, said the time to raise such a challenge to Judge Vaughn had passed: if an issue is not brought up at trial, it is considered waived. “You can’t wait to see how a judge will rule and then say he’s the wrong judge,” Mr. Gillers said.