In Walton v. Arizona, the U.S Supreme Court ruled on a case involving capital punishment and the role of juries in sentencing. The defendant, Jeffrey Alan Walton, was convicted for first-degree murder and kidnapping in an Arizona court. He argued that his death sentence violated his constitutional rights because it allowed a judge rather than a jury to determine whether aggravating factors existed to warrant such a penalty. However, the Supreme Court upheld Walton's death sentence by 5-4 majority vote stating that there is no constitutional requirement for these findings to be made by a jury under Sixth Amendment or Eighth Amendment principles as long as they are reviewed by an appellate court. Furthermore, it held that Arizona’s statutory scheme did not violate due process clause of Fourteenth Amendment which requires heightened reliability in determination of appropriateness of death penalty.

In the dissenting opinion for Walton v. Arizona, Justice Blackmun argued that the majority's decision to uphold Arizona's death penalty statute was a departure from precedent and an abdication of the Court’s responsibility to ensure that capital punishment is administered in a fair and reliable manner. He criticized the majority for deferring too much discretion to trial judges rather than juries in determining whether aggravating factors warrant imposition of death sentences, arguing this violated defendants' Sixth Amendment rights. Furthermore, he disagreed with their interpretation of "especially heinous, cruel or depraved" as sufficiently clear guidelines for imposing capital punishment; instead viewing it as unconstitutionally vague under Eighth Amendment standards against cruel and unusual punishments. Lastly, Justice Blackmun expressed concern about potential arbitrariness in sentencing due to lack of comparative proportionality review by state supreme courts - which could lead to uneven application of death penalties across similar cases.