The "opinion of the Court" -- the plurality opinion -- in Baze v. Rees states in part:
Much of petitioners’ case rests on the contention that they have identified a significant risk of harm that can be eliminated by adopting alternative procedures....Thus spake Justice Roberts. Justice Kennedy and Justice Alito joined in this opinion. See also n. 4 of the plurality opinion, which uses a real-world scientific dispute about lethal injection to support the proposition that assessment of the relative risks of different types of lethal injection "would involve the courts in debatable matters far exceeding their expertise."
Permitting an Eighth Amendment violation to be established on such a showing would threaten to transform courts into boards of inquiry charged with determining “best practices” for executions, with each ruling supplanted by another round of litigation touting a new and improved methodology. Such an approach finds no support in our cases, would embroil the courts in ongoing scientific controversies beyond their expertise [emphasis added], and would substantially intrude on the role of state legislatures... .
Justice Alito, who concurred in Justice Roberts' plurality opinion, wrote a separate concurring opinion in which he said:
Showing merely that a modificationwould result in some reduction in risk is insufficient. Moreover, an inmate should be required to do more than simply offer the testimony of a few experts or a few studies. Instead, an inmate challenging a method of execution should point to a well-established scientific consensus. Only if a State refused to change its method in the face of such evidence would the State’s conduct be comparable to circumstances that the Court has previously held to be in violation of the Eighth Amendment.Daubert, by contrast, dramatically decreased -- ostensibly, in any event -- consensus of scientific opinion as a benchmark for determining the admissibility of scientific evidence in federal trials. (But, again, it must be noted that Daubert involved only -- ostensibly, in any event -- the Court's interpretation of a nonconstitutional rule of evidence, Federal Rule of Evidence 702.)
In a concurring opinion, in which Justice Scalia joined, Justice Thomas stated:
We have neither the authority nor the expertise to micromanage the States’ administration of the death penalty in this manner. There is simply no reason to believe that "unelected" judges without scientific, medical, or penological training are any better suited to resolve the delicate issues surrounding the administration of the death penalty than are state administrative personnel specifically charged with the task.