WASHINGTON — What sort of person would Justice Antonin Scalia have wanted President Obama to name as his successor? We know more than you might think.

In a largely overlooked passage in his dissent from the court’s decision in June establishing a constitutional right to same-sex marriage, he left detailed suggestions.

Avoid “tall-building lawyers,” especially ones who work in skyscrapers in New York. Find someone who did not go to law school at Harvard or Yale. Look for a candidate from the Southwest. Consider an evangelical Christian.

Justice Scalia was criticizing the lack of diversity of the court he sat on, and he did not exclude himself. He was right as a factual matter: Supreme Court justices these days are by many measures remarkably similar, giving the court the insular quality of a private club or a faculty lounge.