On Tuesday, the Supreme Court debated whether Madison belonged in the small but growing category of adults — the intellectually disabled, the mentally ill, those so impaired that they don’t comprehend their punishment — for whom the court has decided the death penalty is unconstitutional.

The task for Bryan A. Stevenson, executive director of the anti-death penalty Equal Justice Initiative in Montgomery, Ala., was to convince the justices they could spare Madison without triggering a flood of challenges from death row inmates claiming not to remember committing their crimes.

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“We recognize that it’s too easy for any offender to say, ‘I don’t remember,’ ” Stevenson said. “But, when you have the kind of disorder that Mr. Madison has . . . then we argue that there is a legitimate basis for arguing that that person cannot rationally understand the circumstances of their execution, and executing them would be inhumane.”

Stevenson said Madison, 68, has had two life-threatening strokes, brain injuries, a documented loss of IQ and an MRI that shows substantial brain damage. “I concede that there are going to be harder cases, there could be harder cases, but under these circumstances, the evidence is quite dramatic,” he said.

Justice Stephen G. Breyer, who has said in the past that he thinks it may be impossible to apply the death penalty in a constitutional way, was sympathetic to Stevenson. But he wondered how the court would write a standard capable of taking care of other cases.

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“There are many, many, many prisoners on death row under threat of execution who are in their 40s, 50s, 60s, 70s, possibly 80s, who have been there for 20, 30, 40 years perhaps,” Breyer said. “So this will become a more common problem.”

Madison himself is a good example of the delay that accompanies capital punishment.

He was arrested in April 1985. Officer Julius Schulte had been called to the Mobile, Ala., home of Madison’s ex-girlfriend, Cheryl Green, to make sure nothing went wrong as Madison retrieved some of his belongings.

But at some point, Madison returned with a gun, and shot Schulte twice in the head, killing him. He also shot Green.

Madison, who is black, had his first conviction thrown out because prosecutors had excluded African Americans from the jury. His second conviction was overturned because prosecutors were found to have introduced inadmissible evidence. He was convicted a third time, and his medical problems began in 2015.

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In Madison’s long legal fight, the Supreme Court at one point said Alabama could proceed with its execution plans. But the justices stopped the process in January 2018, and then accepted his case for oral argument a month later.

Alabama Deputy Attorney General Thomas R. Govan Jr. said the state has provided evidence that Madison can understand why he would be executed. “Nothing about Mr. Madison’s conditions impact the state’s interest in seeking retribution for a heinous crime,” he said.

His biggest ally on the court seemed to be Justice Samuel A. Alito Jr., who asked the toughest questions of Stevenson. (Two other conservatives, Justices Clarence Thomas and Neil M. Gorsuch, did not ask questions.)

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“If a person simply is without memory of his commission of the capital offense, does that in itself render that person incompetent to be executed?” Alito asked. When Stevenson said that wasn’t exactly what he was arguing, Alito said, “I think that’s a question that calls for a yes or no answer.”

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Justice Elena Kagan asked the question another way: “I’m not even sure if this happens ever or whether there’s any sort of physiology behind this, but the idea of a kind of fugue state or a blackout that’s unaccompanied by anything else, does that count as the kind of mental disability that you’re talking about?”

Stevenson said it was not; there would have to be proof of brain damage.

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With only eight justices hearing the case, Chief Justice John G. Roberts Jr. might cast the deciding vote.

He said that Stevenson concedes that simply not remembering the crime is not enough for a defendant to be protected by the court’s decisions against executing the incompetent. And he said Govan conceded that a person may meet those standards by virtue of vascular dementia.

“So all we’re arguing about is whether Mr. Madison himself meets” those standards, Roberts said.