Near the end of this year’s hit Broadway show “What the Constitution Means to Me,” the audience hears a scratchy old recording of an oral argument at the Supreme Court. The year is 1965, and the justices are debating the topic of married women’s right to birth control. Or that’s the idea, anyway; for what feels like an eternity, the nine black-robed men do little but stammer and clear their throats.

“Just listening to all those male voices deciding cases about female bodies, the absurdity of it hit me so hard,” Heidi Schreck, who wrote and performed the one-woman show, told me. “There was a gap in their ability to imagine lives that were very different from their own.”

The scene was on my mind on Tuesday morning as I sat through oral arguments in a landmark trio of L.G.B.T.-rights cases at the Supreme Court. The cases involved three people — two gay men and one transgender woman — who were fired from their jobs, they alleged, because of their sexual orientation or gender identity. All three plaintiffs sued under Title VII of the Civil Rights Act of 1964, which prohibits workplace discrimination on the basis of sex.

For two hours, the justices and the lawyers for both sides debated everything from the meaning of the word “sex” to the nature of congressional intent to the wisdom of sex-segregated bathrooms. I couldn’t help noticing what was missing: the voice, and the perspective, of an openly L.G.B.T. justice. Instead, nine straight people were deciding whether to afford some of the most basic measures of equality to people who identify as gay or transgender and who make up roughly 5 percent of the United States population , according to a Gallup estimate.