In Atkins v. Virginia, the Supreme Court held that the Eighth Amendment ban on cruel and unusual punishment precludes capital punishment for intellectually disabled offenders. Death-penalty states responded with laws defining intellectual disability in various ways. In Hall v. Florida, the Court narrowly struck down the use of a measured IQ of 70 to mark the upper limit of intellectual disability because it created “an unacceptable risk that persons with intellectual disability will be executed.” But the Court was unclear if not inconsistent in its description of an upper limit that would be acceptable. Four dissenting Justices accused the majority not only of misconstruing the Eighth Amendment, but also of misunderstanding elementary statistics and psychometrics. This article uses more complete statistical reasoning to explicate the Court’s concept of unacceptable risk. It describes better ways to control the risk of error than the Court’s confidence intervals, and it argues that, to the extent that the Eighth Amendment allows any quantitative cut score in determining an offender’s intellectual disability, these more technically appropriate methods are constitutionally permissible.

中文翻译：

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致命的统计数据：量化死刑中的“不可接受的风险”†

在阿特金斯诉弗吉尼亚案中，最高法院裁定，第八修正案禁止残忍和不寻常的惩罚，排除了对智障罪犯的死刑。死刑国家通过法律以各种方式定义智力残疾作为回应。在 Hall v. Florida 案中，法院勉强否决了使用 70 的 IQ 来标记智力障碍的上限，因为它造成了“智力障碍者将被处决的不可接受的风险”。但法院在其对可接受的上限的描述中是否不一致，并不清楚。四名持不同意见的法官指责大多数人不仅误解了第八修正案，而且还误解了基本统计数据和心理测量学。本文使用更完整的统计推理来阐释法院的不可接受风险概念。它描述了比法院的置信区间更好的控制错误风险的方法，并且它认为，就第八修正案允许在确定犯罪者的智力障碍时进行任何定量削减分数而言，这些技术上更合适的方法在宪法上是允许的。