ON WRIT OF CERTIORARI TO THE UNITED STATES COURT OF APPEALS FOR THE ELEVENTH CIRCUIT

[May 21, 2026]

PER CURIAM.

The writ of certiorari is dismissed as improvidently granted. It is so ordered .

Page 2SUPREME COURT OF THE UNITED STATES

No. 24-872

ON WRIT OF CERTIORARI TO THE UNITED STATES COURT OF APPEALS FOR THE ELEVENTH CIRCUIT

[May 21, 2026]

JUSTICE SOTOMAYOR, with whom JUSTICE JACKSON joins, concurring.

I concur in the Court's decision to dismiss the writ of certiorari as improvidently granted. I write separately for two reasons. First, based on the evidentiary record and how this litigation proceeded below, I explain why the Court should not and cannot use this case to address how courts must analyze multiple IQ scores under Atkins v. Virginia , 536 U. S. 304 (2002). Second, I point out how the principal dissent's discussion of this Court's precedents and the scientific consensus about how courts should evaluate multiple IQ scores is incomplete and potentially misleading.

In 1998, Joseph Smith was convicted of first-degree murder. At his sentencing hearing, Smith introduced evidence of intellectual disability, including an IQ score of 72 and testimony from the test’s administrator explaining that the test's standard error of measurement indicated Smith's IQ could be as low as 69 or as high as 75.¹ Smith alsoPage 3 introduced his school records, which showed that he was previously administered two IQ tests resulting in scores of 75 and 74 and that he was classified as ''educable mentally retarded'' in 7th grade. Smith v. State , 71 So. 3d 12, 19–20 (Ala. Crim. App. 2008). At the time of Smith's sentencing, this Court had held that it did not violate the Eighth Amendment to execute an intellectually disabled person so long as the sentencers considered mitigating evidence of the defendant’s intellectual disability among other aggravating or mitigating evidence. See Penry v. Lynaugh , 492 U. S. 302, 328, 330–335 (1989). The jury in Smith’s case returned an advisory verdict recommending the death penalty, which the trial judge imposed. The Alabama Supreme Court affirmed Smith’s sentence.

A few years later, this Court held in Atkins v. Virginia , 536 U. S. 304 (2002), that it violates the Eighth Amendment to execute an individual who is intellectually disabled. In so holding, the Court largely left it to the States to ''develo[p] appropriate ways to enforce'' this limitation. Id ., at 317. The Alabama Supreme Court responded by adopting a definition of intellectual disability that requires the defendant to prove three prongs, all by a preponderance of the evidence: (1) 'significantly subaverage intellectual functioning (an IQ of 70 or below)'; (2) 'significant or substantial deficits in adaptive behavior'; and (3) manifestation of “these problems . . . during the developmental period (i.e., before the defendant reached age 18).” Ex parte Perkins , 851 So. 2d 453, 456 (2002).

After Atkins and Perkins were decided, Smith petitioned for postconviction relief in Alabama state court, alleging that he is intellectually disabled under Alabama's definition and that his execution would violate the Eighth Amendment. The trial court denied Smith's request for an Page 4evidentiary hearing and his petition, the Alabama Court of Criminal Appeals affirmed that decision, and the Alabama Supreme Court denied review.

Smith next petitioned for federal habeas relief in the District Court for the Southern District of Alabama. The District Court initially denied his petition, but the Eleventh Circuit reversed. The Court of Appeals held that the District Court wrongly deferred to the Alabama Court of Criminal Appeals' decision under 28 U. S. C. §2254(d) and remanded for the District Court to conduct a de novo inquiry into whether Smith is intellectually disabled under Alabama’s definition of intellectual disability. Smith v. Campbell , 620 Fed. Appx. 734 (2015). Alabama did not file a petition for a writ of certiorari to this Court.

On remand in the District Court, Alabama and Smith agreed to an evidentiary hearing. See Smith v. Thomas , No. 1:05–cv–00474 (SD Ala., July 1, 2016), ECF Doc. 75. Both parties hired experts to administer new IQ tests: Dr. King for the State and Dr. Fabian for Smith. On the test administered by King, Smith scored a 74 with a 95% confidence interval of 70 to 79. On the test administered by Dr. Fabian, Smith scored a 78 with a 95% confidence interval of 72 to 83. At this point, Smith had obtained five IQ scores ranging from 72 to 78. The District Court then admitted expert reports from King, Fabian, and an additional expert proffered by Smith, and heard testimony from all three as to whether Smith is intellectually disabled.

The experts each opined on Smith's intellectual functioning. The State’s expert, King, stated in his report that a score of 74 'would technically place [Smith in] the borderline range of intellectual functioning,” but that the score “is not reflective . . . of his true intellectual functioning,” which King described as “in the low average range of ability.” 2 App. 596. King explained that 'a single . . . IQ score' isPage 5 comprised of multiple subscores, which reflect different aspects of one's intellectual functioning, and a final score “needs to be additionally parsed in order to look at whether there is subtest scatter or whether there is consistency.' Id ., at 596-597. In the IQ test that King administered, the scatter in Smith's subscores was, in King's view, more 'indicative of . . . a learning disabilit[y]' than of intellectual disability. Id ., at 598. King testified that, in his view, Smith did not have significantly subaverage intellectual functioning based “on all the data that [he] collected, all the records that [he] reviewed” and “all of the IQ tests that have been compiled over a lengthy period of time.” 1 id ., at 271. He also explained that his conclusion was based in part on Smith's 'presentation to' and 'ability to interact' with King. Id ., at 271–272.

Smith’s experts similarly reviewed all of Smith’s scores and records, but came to different conclusions. Fabian testified that several of Smith’s prior scores were “in the range for intellectual disability,' id ., at 244, and that, overall, Smith 'meets the intellectual deficit prong of the intellectual disability definition,' id ., at 179-180. Fabian explained that even though Smith’s scores were above 70, one “need[s] to consider those IQ scores with the other areas of functioning,' such as his adaptive functioning, including evidence of his 'academic achievement' and 'executive functioning.” Id ., at 180. Together, those latter considerations showed that, “cognitively[, Smith is] impaired in a number of areas' and that, according to Fabian, Smith's IQ scores 'in total can be considered consistent with significant limitations in intellectual disability.” Ibid . Smith's second expert, too, testified that Smith’s scores were “in the range of what would be considered mild intellectual disability,' 'particularly' when 'consider[ing] the standard error of measurement.” Id ., at 111; see also 3 id ., at 875.

In assessing Smith’s intellectual functioning, the District Court also considered a report by the expert who had Page 6administered the 1998 test in which Smith scored a 72 with a standard error range of 69 to 75. That expert concluded that Smith's score 'places him at the 3rd percentile in comparison to the general population,' and that Smith ''operates between the Low Average and Mentally Retarded range'' but ''at a level closer to those individuals who would be considered mentally retarded.'' Smith v. Dunn , Civ. Action No. 05–00474 (SD Ala., Aug. 17, 2021), App. to Pet. for Cert. (Pet. App.) 73a.

Based on all the evidence, the District Court found that whether Smith 'qualifies as having significantly subaverage intellectual function[ing]' was 'not clear' and that this was a “close case.” Id. , at 74a. The court acknowledged that King “testified that if there are multiple sources of IQ over a long period of time[,] it contributes to the construct of validity indicating what a true IQ score is for an individual” and that “multiple IQ scores” in Smith’s case “place him in the borderline range, functioning just above intellectual disability.” Id. , at 70a. However, the District Court did 'not find [this evidence] strong enough to conclude that Smith is not intellectually disabled without considering evidence of his adaptive deficits” because Smith “did not consistently score so high that the [District] Court [wa]s confident that the lowest score can be thrown out as an outlier or that the standard error for the tests can be disregarded.' Ibid . The District Court observed that “at best Smith[’s] intelligence falls at the low end of the Borderline range of intelligence and at worst at the high end of the required significantly subaverage intellectual functioning.” Id. , at 74a. It therefore decided to consider 'additional evidence,' including evidence about 'whether Smith suffers from significant or substantial deficits in adaptive behavior,” to assess whether Smith is intellectually disabled. Ibid.

From there, the District Court analyzed evidence of Smith's adaptive deficits, which included Smith's school records, testimony from Smith's family members aboutPage 7 Smith's abilities, testimony from Smith himself, and the expert opinions of King and Fabian. Id ., at 75a-92a.² The District Court also considered the results of other psychological tests, which related to both the intellectual-functioning and adaptive-functioning prongs. Id ., at 90a–92a.

After weighing all the evidence, the District Court found that “Smith has shown by a preponderance of the evidence that he has significantly subaverage intellectual functioning and significant deficits in adaptive behavior.” Id ., at 92a. The court also found that Smith’s intellectual- and adaptive-functioning issues “clearly arose before he was 18 years of age.' Id ., at 96a. Based on these findings, the court concluded that Smith “is intellectually disabled and cannot constitutionally be executed.” Id ., at 96a–97a.

The Eleventh Circuit initially affirmed, but this Court vacated that decision because its basis was “unclear.” Hamm v. Smith , 604 U. S. 1, 2 (2024) ( per curiam ). The Court explained that “the Eleventh Circuit’s opinion might be read to afford conclusive weight to the fact that the lower end of the standard-error range for Smith’s lowest IQ score is 69,” which 'would suggest a per se rule that the lower end of the standard-error range for an offender’s lowest score is dispositive” of the intellectual-functioning prong. Ibid . Alternatively, the opinion could be read to 'suggest a more holistic approach to multiple IQ scores that considers the relevant evidence, including as appropriate any relevant expert testimony.” Ibid . This Court noted that it 'has not specified how courts should evaluate multiple IQ scores,” and asked the Eleventh Circuit to clarify its holding. Ibid . On remand, the Eleventh Circuit answered that it had used a ''holistic approach.'' Smith v. Commissioner, Ala.

Page 8Dept. of Corrections , No. 21–14519 (Nov. 14, 2024) ( per curiam ), Pet. App. 2a. It also “unambiguously reject[ed] any suggestion that a court may ever conclude that a capital defendant suffers from significantly subaverage intellectual functioning based solely on the fact that the lower end of the standard-error range for his lowest of multiple IQ scores is 69.” Ibid . It then affirmed the District Court's decision, explaining that the District Court had properly considered “Smith’s IQ test results, taken together and in context of expert testimony,' and that its factual findings were not clearly erroneous. Id ., at 5a.

Alabama filed a petition for a writ of certiorari proposing two questions: First, “[w]hether, under a proper application of Atkins , a State can require a claimant to prove an IQ of 70 or less by a preponderance of the evidence”; and second, “[w]hether courts evaluating multiple IQ scores must find that every valid score of ‘about’ 75 or less supports an Atkins claim.” Pet. for Cert. i. This Court declined to grant either question, and instead granted a question raised by the United States on the last two-and-a-half pages of its amicus brief: 'Whether and how courts may consider the cumulative effect of multiple IQ scores in assessing an Atkins claim.' Brief for United States as Amicus Curiae on Pet. for Cert. I; see id ., at 20–22. The United States did not identify any split among the lower courts on this issue. See id ., at 20–22.

The Court is not equipped in this case to provide any meaningful guidance on how courts should assess multiple IQ scores. All the parties here agree that the Eighth Amendment does not prescribe a single formula for weighing multiple IQ scores. All the parties also agree that Atkins gave States the primary role in “developingPage 9 appropriate ways to enforce' Atkins . 536 U. S., at 317. Although the parties offer to this Court a variety of approaches to assessing multiple IQ scores that States could adopt, the litigation below did not focus on whether a precise methodology exists that courts must use. Without the benefit of an evidentiary record or decisions below trained on the specific theories now advanced by the parties, this Court rightly concludes that it should not provide more detailed guidance beyond what this Court’s cases have previously said.

To start, and most significantly, the parties agree that there is no single approach to weighing multiple IQ scores. Alabama here disclaims any “single, mechanical rule . . . for aggregating multiple IQ scores.” Reply Brief 12 (internal quotation marks omitted; ellipsis in original). It instead offers a rule that a factfinding court must consider the 'cumulative effect” of multiple IQ scores, by which it means that the scores must be “combine[d] to prove an IQ of 70 or below.” Id ., at 1, 10. Alabama suggests that courts could do so using one of several methods, such as taking the median, examining the 'overlap among each score's error range,” calculating a composite score, taking the average, or looking only at the highest score. Id ., at 10-12, 19. Still, it acknowledges that there is no “consensus over whether and how to evaluate the cumulative effect of multiple IQ scores.' Brief for Petitioner 28.

The United States agrees that “the Eighth Amendment” does not 'prescrib[e] a specific approach to analyzing multiple IQ tests.” Brief for United States as Amicus Curiae 19. It notes that it is 'possible' to combine multiple scores into a composite score or into a “single range,” but contends only that “a court may take stock of the full range of . . . IQ scores,” not how a court must do so. Id ., at 18–19. It also emphasizes that if a court considered multiple scores or a combination of those scores, such as a composite score, thePage 10 inquiry would '[o]f course . . . fall to the factfinder to assess and weigh this sort of expert analysis.” Id. , at 19.

Smith, for his part, contends that courts must assess multiple IQ scores 'holistically,' which includes 'considering those scores in light of other evidence—particularly expert testimony—regarding the scores’ validity and meaning, and other evidence of the claimant’s intellectual functioning.” Brief for Respondent 2. Smith does not disagree with Alabama and the United States, however, that as part of that holistic analysis, courts could consider an aggregation of scores, such as a composite score, if one is presented.

Thus, despite discussing different methods by which courts could assess multiple IQ scores, the parties all appear to agree there is no particular method by which courts must consider multiple scores.

The Court’s review is further complicated by the fact that the issue of how to consider multiple IQ scores was neither meaningfully raised nor passed upon below. In the District Court, Alabama never argued that the court must, as a matter of law, combine all IQ scores using any particular method (or set of methods) to assess whether an Atkins claimant has proven significantly subaverage intellectual functioning. See Respondent's Post-Hearing Brief, ECF Doc. 129, pp. 36-46. Nor did Alabama argue that the District Court must base its finding of intellectual functioning solely on Smith’s IQ scores, without considering evidence of Smith’s academic performance and adaptive functioning as well. See id ., at 36 (arguing that Smith's school records show he does not meet the intellectual-functioning prong, rather than asking the District Court to ignore those records). Instead, Alabama urged the District Court to apply Alabama's state-law standard for assessing intellectual disability, which it explained does not “preclude consideration of other evidence of intellectual disability, including Page 11testimony regarding adaptive deficits[,] when a person has an IQ over 70.” Id ., at 4.

In fact, none of the experts, not even the State’s expert, combined Smith’s scores using any method that Alabama now claims is necessary. Not one of the experts calculated a composite score, used the mean or median, examined the “overlap” of the scores’ error ranges, or relied solely on the highest score. Nor did any expert testify that using such methods was the most scientifically sound way to evaluate Smith's intellectual functioning. Instead, all three considered all the scores in addition to other evidence and used their own clinical judgment to render conclusions about Smith's intellectual functioning. In other words, each expert assessed the scores holistically.

Nor did Alabama appeal the District Court's determination on this basis. In its brief to the Eleventh Circuit, Alabama argued that the District Court improperly shifted the burden of proof onto the State to prove that Smith was not intellectually disabled and that its factual determinations were clearly erroneous. At no point did Alabama contend that the District Court erred by failing to combine Smith’s scores using one of the methods it now claims is required.

Unsurprisingly, then, neither the District Court nor the Eleventh Circuit specifically addressed whether a court must consider the “cumulative effect” of Smith’s IQ scores by combining them using a specific method, or whether one method is better than another, or even how a court should go about deciding which method is preferable. Instead, based on the arguments and evidence raised, the Eleventh Circuit held that the District Court did not err in its ''holistic'' consideration of Smith's scores and that its factual determination that Smith has significant subaverage intellectual functioning was not clearly erroneous “based on the complete record, including any relevant expert testimony.” Pet. App. 2a.

Page 12What is more, it does not appear that a single state legislature or court or Federal Court of Appeals has adopted Alabama’s proposed rule that courts must combine multiple IQ scores using any one method (or a set of methods); nor has any adopted a rule prohibiting courts from assessing multiple scores holistically without combining them, just as the District Court did here. This Court is therefore right to exercise caution and decline to adopt any such rules now.³

C

The principal dissent claims that the Court should have taken this opportunity to provide “much-needed guidance” to lower courts. Post , at 1 (opinion of ALITO, J.). At the outset, there is no evidence that the lower courts are desperate for guidance; there is no split and neither state courts nor federal courts have expressed substantial confusion over how to assess multiple IQ scores. See, e . g ., Black v. Carpenter , 866 F. 3d 734, 743-749 (CA6 2017) (affirming the District Court's review of 10 scores and expert testimony interpreting those scores); Jackson v. Payne , 9 F. 4th 646, 653 (CA8 2021) (similar). Nor is there a barrage of Atkins cases involving multiple IQ scores; in the 12 years since Hall v. Florida , 572 U. S. 701, was decided, Smith's counsel identifies only 43 Atkins cases across the country in which courts evaluated multiple IQ scores. Brief for Respondent 9, and n. 1. 4Page 13 The guidance the principal dissent wishes to provide appears to be, in part, that courts should consult the methods outlined in the American Psychological Association's Handbook of Intellectual and Development Disabilities (APA Handbook). Post , at 8. It is hard to imagine, however, that courts need this lesson, given that this Court’s cases have repeatedly explained that “[i]n determining who qualifies as intellectually disabled, it is proper to consult the medical community's opinions,' Hall , 572 U. S., at 710, including “leading diagnostic manuals,” Moore v. Texas , 581 U. S. 1, 13 (2017); see Atkins , 536 U. S., at 318 (considering the medical community’s framework).

The principal dissent apparently seeks to go further and wants this Court to provide more granular guidance about which specific methods of assessing multiple scores are acceptable. Post , at 8-10. As described above, this Court cannot differentiate between methods because these various methods were not raised in the litigation below.

Proceeding without a more developed record or lowercourt opinions is especially perilous. That is because the differences between methods used to assess multiple IQ scores raise complicated questions on which even experts may disagree. As one example, the principal dissent, citing several studies, argues that 'when an individual has multiple IQ scores, the 'higher scores are likely to be more indicative' of a person's intelligence than the lower scores.' Post , at 11. Yet, the American Association on Intellectual and Developmental Disabilities (AAIDD) explains that 'when IQ scores are all close to the boundary of intellectual disability, the ‘true’ score may actually be even lower than the reported scores.” Brief for AAIDD et al. as Amici Curiae (AAIDD Brief ) 26. Due to the statistical concept of Page 14regression to the mean, the AAIDD elaborates, when an individual’s scores are “grouped far away from the mean score of 100 used on most IQ tests[,] it is a statistical indicator that the individual's 'true' score is likely to be even farther away from the mean.' Ibid . (emphasis deleted); see also D. Watson, Intelligence Testing, in The Death Penalty and Intellectual Disability 124 (E. Polloway ed. 2015) ('[I]t is inappropriate to simply accept, in a rote fashion, [a] higher score in the false belief that one can never score higher than their true IQ but can always score poorer in the face of limited effort'). There is no reason for this Court to leapfrog the experts, state courts, and federal lower courts to provide conclusive guidance at this level of detail in the first instance.

Thus, for the reasons given above, the Court is correct today to dismiss this case as improvidently granted.

Despite the principal dissent's professed concern that lower courts lack sufficient guidance from this Court to analyze multiple IQ scores in general, it seems that the core of the dissent's dissatisfaction is rather with the District Court's specific conclusion in this case that Smith is intellectually disabled and thus cannot be executed. See post , at 10. Even on these case-specific grounds, the dissent is mistaken. I therefore write to explain why the District Court's holistic method of reviewing multiple IQ scores is consistent with this Court's precedents, the medical community's diagnostic framework, and Alabama state law. Furthermore, the District Court's factual finding that Smith has significantly subaverage intellectual functioning, and its ultimate conclusion that Smith is intellectually disabled, is neither properly before the Court nor clearly erroneous.⁵

To start, the principal dissent claims that the lower courts misinterpreted Hall and Moore . They did not. This Court has not previously addressed the method by which 'courts should evaluate multiple IQ scores,' Hamm , 604 U. S., at 2, but it has confronted several cases involving multiple scores. The District Court's holistic review below was consistent with those precedents.

In Hall v. Florida , 572 U. S. 701, the Atkins claimant had seven valid scores between 71 and 80, and Florida sought to execute him based on Florida precedent requiring an IQ score below 70 before allowing additional evidence of intellectual disability. 572 U. S., at 707.⁶ The lower courts had denied relief, but this Court reversed, reasoning that 'Florida’s rule disregard[ed] established medical practice in two interrelated ways.” Id ., at 712. First, “[i]t [took] an IQ score as final and conclusive evidence of a defendant's intellectual capacity, when experts in the field would consider other evidence.” Ibid . Second, it 'relie[d] on a purportedly scientific measurement of the defendant’s abilities, his IQ score, while refusing to recognize that the score is, on its own terms, imprecise.” Ibid . The Court acknowledged that “the analysis of multiple IQ scores jointly is a complicated endeavor,' but that '[e]ven when a person has taken multiple tests, each separate score must be assessed using the [standard error of measurement].” Id ., at 714.

In reaching this conclusion, the Court observed that because a given IQ “test itself may be flawed, or administered Page 16in a consistently flawed manner, multiple examinations may result in repeated similar scores, so that even a consistent score is not conclusive evidence of intellectual functioning.” Ibid. From this, the Court reasoned that a court may not refuse to consider additional evidence beyond IQ scores, such as evidence of 'the defendant's failure or inability to adapt to his social and cultural environment, including medical histories, behavioral records, school tests and reports, and testimony regarding past behavior and family circumstances,” if “the medical community accepts that [such] evidence can be probative of intellectual disability, including for individuals who have an IQ test score above 70.” Id ., at 712. Thus, the Court held that Hall must “have the opportunity to present evidence of his intellectual disability, including deficits in adaptive functioning over his lifetime,” even though his seven IQ scores were all above 70. Id ., at 724.

Moore v. Texas , 581 U. S. 1, also involved an Atkins claimant with multiple valid scores: a 74 and a 78. See 581 U. S., at 10.⁷ Applying Hall , the Court reasoned that 'Moore's score of 74, adjusted for the standard error of measurement, yields a range of 69 to 79,” and “[b]ecause the lower end of Moore’s score range falls at or below 70, the [Texas court] had to move on to consider Moore’s adaptive functioning” and could not “end the intellectual-disability inquiry, one way or the other, based on [the] IQ score' alone. 581 U. S., at 14–15.

The principal dissent claims that the District Court contravened Moore by 'deflat[ing] its estimate of Smith's IQ based on details about his” adaptive deficits. Post , at 16. That misunderstands both the Court's decision in Moore and the District Court’s decision below.

Page 17In Moore , the Texas courts had discounted the lower end of the standard error range for Moore's score of 74 because he 'was likely exerting poor effort and experiencing depression at the time the test was administered.' 581 U. S., at 25 (ROBERTS, C. J., joined by THOMAS and ALITO, JJ., dissenting). The Court rejected that reasoning because “the presence of other sources of imprecision in administering the test to a particular individual . . . cannot narrow the test-specific standard-error range.' Id ., at 15 (majority opinion). The Court held that, 'in line with Hall , . . . courts [must] continue the inquiry and consider other evidence of intellectual disability where an individual's IQ score, adjusted for the test's standard error, falls within the clinically established range for intellectual-functioning deficits.” Id ., at 15. Because Moore had a score of 74, which 'yield[ed] a range of 69 to 79,' the Court 'requir[ed] the [Texas court] to move on to consider Moore's adaptive functioning in light of his IQ evidence.” Id ., at 14.

Here, the District Court did not discount the lower or higher end of the standard-error range for Smith’s scores because of his adaptive deficits; rather, it accepted the full ranges as reflective of what Smith’s IQ was likely to be. See Pet. App. 70a (“Smith did not consistently score so high that the Court is confident that . . . the standard error for the tests can be disregarded”); id ., at 68a (“It remains clear that the Court should consider the standard error inherent in IQ tests'). It considered all of Smith's scores and their respective standard errors, some of which fell into the clinically established range for intellectual-functioning deficits, and concluded that 'additional evidence must be considered, including testimony on [Smith's] adaptive deficits[,] to determine whether Smith is intellectually disabled.' Id ., at 74a. That is the same analysis that Hall endorsed and that Moore undertook. The District Court did not deflate a particular score, but instead concluded, based on error ranges Page 18and other evidence of cognitive function, that Smith's intellectual functioning is significantly subaverage.

Thus, in both Hall and Moore , this Court confronted Atkins claimants with multiple scores above 70 (and none below 70), yet still held that courts should consider the scores in light of 'additional evidence of intellectual disability, including testimony regarding adaptive deficits.” Hall , 572 U. S., at 723. At no point did the Court require, or even suggest, that courts must analyze the scores by combining them using any specific method that the principal dissent contends is necessary. The District Court's holistic approach was thus squarely in line with Hall and Moore .

The principal dissent also claims that the District Court’s holistic approach 'contravened psychology' and 'statistics.' Post , at 2. The District Court's analysis, however, was entirely consistent with 'the medical community's diagnostic framework.” Hall , 572 U. S., at 721. When a person has multiple IQ scores, the APA Handbook explains that 'clinicians may benefit from evaluating the 95% confidence intervals for each score and collectively interpreting the complete set of scores using clinical judgment.” R. Floyd, R. Farmer, W. Schneider, & K. McGrew, Theories and Measurement of Intelligence, in 1 APA Handbook of Intellectual and Developmental Disabilities 415 (L. Glidden ed. 2021). The District Court here evaluated Smith’s scores in light of their confidence intervals and took into account the clinical judgment of the experts who each interpreted those scores. See Brief for American Psychological Association et al. as Amici Curiae 22 (APA Brief) (stating that the decision below is 'fully consistent' with its clinical principles). Further, the consensus within the medical community is that there is not one “single, mandatory empirical method,” or one set of mandatory methods, for 'considering multiple scores' because clinicians must consider the 'validity of Page 19each test score and the convergence of that score with other scores and qualitative information.' AAIDD Brief 24.⁸ Moreover, the District Court’s consideration of adaptive deficits is consistent with the consensus within the medical community, which has made clear that the existence of multiple IQ scores above 70 does not necessarily end the inquiry entirely. Both the APA and the AAIDD emphasize that 'IQ test scores cannot stand alone' and 'must be considered alongside other data that inform a clinician’s assessment both of intellectual functioning and the other diagnostic criteria.” Id ., at 5; American Psychiatric Association, Diagnostic and Statistical Manual of Mental Disorders (DSM) p. 42 (5th ed. text rev. 2022) (“[U]sing [IQ scores] as the sole criteria for the diagnosis of an intellectual developmental disorder is insufficient'). As Hall emphasized, '[i]t is not sound to view a single factor,' such as IQ scores, 'as dispositive of a conjunctive and interrelated assessment,' and ''[a] person with an IQ score above 70 may have such severe adaptive behavior problems . . . that the person's actual functioning is comparable to that of individuals with a lower IQ score.'' 572 U. S., at 723 (quoting DSM-5, p. 37 (5th ed. 2013)). Therefore, according to medical consensus, when IQ scores are “close to the boundary of intellectual disability,” a “clinician must conduct a detailed review of qualitative reports of the individual’s skills and behavior ‘focusing heavily on the functional assessment of what the person actually does’ and on how the person interacts with the environment . . . to create the most accurate picture of Page 20the person’s day-to-day intellectual functioning.” AAIDD Brief 28 (citing R. Schalock & R. Luckasson, Clinical Judgment 29 (2d ed. 2014)); see also AAIDD Brief 28-29 (collecting additional citations). The District Court was thus following the framework of the medical community, endorsed by this Court's precedents, when it found that although Smith's IQ scores made this a 'close case,' Smith had proven by a preponderance of the evidence that he had significantly subaverage intellectual functioning. Pet. App. 91a, 96a.⁹

The principal dissent further claims that whether the District Court’s analysis comported with Alabama law does not bear upon whether Smith’s death sentence violated the Constitution. Post , at 19-20. Whether Smith's execution would violate the Eighth Amendment under Atkins , however, is dependent on Alabama’s definition of intellectual disability because Atkins ''le[ft] to the State[s] the task of developing appropriate ways to enforce [this] constitutional restriction.'' 536 U. S., at 317 (second alteration in original); see also Brumfield v. Cain , 576 U. S. 305, 308, 314 (2015) (applying state-law definition to determine whether claimant was intellectually disabled for Atkins purposes). The parties here have rightly proceeded on this understanding. Brief for Petitioner 23; Brief for Respondent 39; Brief for United States as Amicus Curiae 25; see also Page 21Petitioner’s Post-Hearing Brief, ECF Doc. 129, p. 2 ('[F]ederal courts must look to and apply Alabama's definition of intellectual disability”).

Moreover, the District Court’s holistic analysis comports with Alabama law, which has no statute or Alabama Supreme Court decision prescribing how courts must consider multiple IQ scores. See Thomas v. Allen , 607 F. 3d 749, 757 (CA11 2010) (“There is no Alabama case law stating that a single IQ raw score, or even multiple IQ raw scores, above 70 automatically defeats an Atkins claim when the totality of the evidence (scores) indicates that a capital offender suffers subaverage intellectual functioning'). Alabama appellate courts instead recognize that “a court should look at all relevant evidence in assessing an intellectual-disability claim and that no one piece of evidence, such as an IQ test score, is conclusive as to intellectual disability.” Reeves v. State , 226 So. 3d 711, 729 (Ala. Crim. App. 2016). 'Conflicting expert testimony” with respect to an Atkins claimant's intellectual functioning ''is always a question for the finder of fact to determine.'' 226 So. 3d., at 741. The District Court's analysis here fully comported with these principles.

At bottom, the principal dissent’s central complaint with the lower courts’ decisions is not truly with the method by which the District Court analyzed the scores. Rather, the dissent looks at Smith’s five scores at face value and cannot fathom that Smith has significantly subaverage intellectual functioning. The Court rightly decides not to 'upset the considered judgment[s] of the forensic psychologist[s] that the factfinding court deemed the most credible based on [the dissent’s] own interpretation of a few sentences excised from medical texts.' Moore , 581 U. S., at 33 (ROBERTS, C. J., joined by THOMAS and ALITO, JJ., dissenting).

The District Court's factual determination also cannot be reversed unless it is clearly erroneous. 'If the district Page 22court’s account of the evidence is plausible in light of the record viewed in its entirety,” an appellate court “may not reverse it even though convinced that had it been sitting as the trier of fact, it would have weighed the evidence differently.” Anderson v. Bessemer City , 470 U. S. 564, 573–574 (1985). When factual findings 'are based on determinations regarding the credibility of witnesses,” such as the experts here, clear-error review “demands even greater deference to the trial court’s findings.” Id ., at 575. Indeed, three of the dissenting Justices have previously agreed that ''[b]ecause there often is no single, accurate psychiatric conclusion,'' it is 'importan[t]' to allow the ''primary factfinder[]' to 'resolve differences in opinion . . . on the basis of the evidence offered by each party.'' Moore , 581 U. S., at 32 (ROBERTS, C. J., joined by THOMAS and ALITO, JJ., dissenting) (third alteration and ellipsis in original).

Here, neither Alabama nor the United States seriously contends that the District Court's finding was clearly erroneous. For good reason: It was not. The District Court held an evidentiary hearing and carefully weighed the evidence, including the raw IQ scores, each score's standard error range, expert testimony about interpreting those scores, and much more. The court ultimately found that Smith has significantly subaverage intellectual functioning and is intellectually disabled. On my review of the record, this determination was correct, or, at the very least, plausible. See APA Brief 22 ('The IQ test scores in this case fall comfortably within the range within which a clinician could reasonably conclude . . . that Smith satisfied' the intellectualfunctioning prong of Alabama’s definition). In the principal dissent's view, that determination was incorrect. Either way, this Court is not as equipped as the District Court to appreciate all the evidence.

In any event, this Court did not grant certiorari to decide whether the Eleventh Circuit properly applied a preponderance of the evidence standard. Nor did the Court grant Page 23certiorari to decide whether the District Court's factual determination was clearly erroneous. Given that, the Court today rightly declines to reweigh the evidence underlying the District Court’s determination.

Ultimately, as this Court has recognized, “[i]ntellectual disability is a condition, not a number' and the ''the diagnosis of [intellectual disability] is intended to reflect a clinical judgment rather than an actuarial determination.'' Hall , 572 U. S., at 723 (second alteration in original). In close cases such as this one, the inquiry may well involve a substantial amount of evidence, but that inquiry is nevertheless critical to avoid the “unacceptable risk that persons with intellectual disability will be executed” contrary to the Eighth Amendment. Id. , at 704.

* * *

In cases presenting multiple IQ scores, courts should continue to consider multiple IQ scores in light of this Court’s precedents and ''the views of medical experts.'' Moore , 581 U. S., at 5. If a conflict among the States or lower courts emerges and a case properly presents the issue, it may be appropriate for this Court to weigh in with more specific guidance about the permissible method or methods by which courts must analyze such scores. The Court rightly decides that it is inappropriate to do so in this case. I therefore concur in the decision to dismiss the writ of certiorari as improvidently granted.

Page 24SUPREME COURT OF THE UNITED STATES

No. 24-872

ON WRIT OF CERTIORARI TO THE UNITED STATES COURT OF APPEALS FOR THE ELEVENTH CIRCUIT

[May 21, 2026]

JUSTICE THOMAS, dissenting.

In 1997, Joseph Clifton Smith murdered Durk Van Dam. The trial court, accepting the jury's recommendation, sentenced Smith to death. Smith lost his appeal in 2001. But a year later, in Atkins v. Virginia , 536 U. S. 304 (2002), this Court held for the first time that convicted murderers like Smith cannot be executed if they are deemed insufficiently intelligent, which the Court suggested would require that they had an IQ of 70 or below. Id ., at 308-309, and n. 3, 316–321. Such persons could not be executed, the Court said, even if they “know the difference between right and wrong,” even if they “are competent to stand trial,” and even if they are intelligent enough to deserve other 'criminal sanctions.” Id ., at 318. The Court did not pretend that the Constitution had ever been understood to impose such a rule. Id ., at 340–341 (Scalia, J., dissenting). Just 13 years earlier, it had acknowledged the opposite. Penry v. Lynaugh , 492 U. S. 302, 330–335 (1989). But the Court set aside the Constitution and imposed a new rule anyway. The result was predictable: To avoid execution, Smith tried to convince courts that he is not intelligent enough to be executed.

Today, the Court rewards Smith’s efforts. It dismisses the State's petition challenging the lower courts' vacatur ofPage 25 his death sentence under Atkins . But Smith is not insufficiently intelligent to be executed. He can read at an 11thgrade level. He took five IQ tests and did not once receive a score of 70 or below, instead scoring 75, 74, 72, 78, and 74. The lower courts held that he could not be executed based only on the hypothetical possibility that these IQ scores were all wrong and that his IQ is in fact 70 or below. I join JUSTICE ALITO’s opinion because it persuasively explains why that approach is statistically indefensible.

As this case shows, though, Atkins has bred only confusion and absurdity. Nothing in the text or history of the Constitution supports Atkins . It should be overruled.

In 1997, just two days after being released from custody for burglary, Joseph Clifton Smith murdered Durk Van Dam. Smith plotted with his friend Larry Reid to rob Van Dam, whom they heard was carrying cash. They lured Van Dam to an isolated location. There, Smith and Reid beat Van Dam and attacked him with a power saw, eventually killing him. Smith and Reid then divided the money that they stole from Van Dam. Smith told one person that he had hit Van Dam on the head and cut him, and he told another that he had hit, cut, and stabbed Van Dam.

The police discovered Van Dam’s badly mutilated body in a wooded area. He had injuries from the saw on his neck, shoulder, and back. He also suffered a hemorrhage under his scalp, broken ribs, and brain swelling. The broken ribs caused one of Van Dam's lungs to collapse. A forensic pathologist testified that 35 blunt-force injuries caused his death. He died trying to defend himself.

A jury convicted Smith of murdering Van Dam and recommended that he be sentenced to death. The trial court found three aggravating circumstances and no significant mitigating circumstances. The three aggravatingPage 26 circumstances were that Smith was on leave from his term of imprisonment for burglary at the time of the murder; that the murder occurred during a robbery; and “that the murder was especially heinous, atrocious, or cruel.” Smith v. State , 795 So. 2d 788, 797, n. 1, 841-842 (Ala. Crim. App. 2000) ( per curiam ). As for mitigating circumstances, the trial court rejected Smith's arguments that his bad upbringing or lack of intelligence justified a sentence other than death. It explained that Smith's upbringing did not ''justify a[n] act of senseless rage directed at an innocent human being.'' Id. , at 841. And it found that Smith's ''lack of intelligence is not an excuse for murder, especially in the context of this case.'' Ibid . Smith 'knew he had,' in his words, “F___ Up,” and, “while in control [of himself,] he savagely attacked” Van Dam. Ibid . (internal quotation marks omitted). The trial court accepted the jury’s recommendation and sentenced Smith to death.

The Alabama Court of Criminal Appeals affirmed the conviction and death sentence. Id. , at 842. Both the Supreme Court of Alabama and this Court denied certiorari. Ex parte Smith , 795 So. 2d 842 (2001); Smith v. Alabama , 534 U. S. 872 (2001).

B

A year later, this Court's decision in Atkins opened a new avenue for convicted murderers such as Smith to challenge their death sentences.

Atkins arose out of another robbery and murder. Daryl Atkins and a friend abducted and robbed a United States airman named Eric Nesbitt. 536 U. S., at 307; id ., at 338 (Scalia, J., dissenting). After abducting and robbing him, Atkins shot Nesbitt eight times, killing him. Id. , at 307 (majority opinion). The jury found Atkins guilty of capital murder. At the penalty phase, the jury heard “extensive evidence' of Atkins's 'alleged mental retardation,' including testimony from a psychologist that Atkins “was ‘mildlyPage 27 mentally retarded'' with an 'IQ of 59,' and testimony from another psychologist who concluded that Atkins was 'of 'average intelligence, at least.'' Id ., at 308–309; id ., at 338– 339 (Scalia, J., dissenting). The jury also learned that Atkins had “16 prior felony convictions for robbery, attempted robbery, abduction, use of a firearm, and maiming.” Id. , at 339. Atkins had previously attacked a different victim with a gun, “knocked her to the ground, and then helped her up, only to shoot her in the stomach.” Ibid. After hearing all the evidence, the jury sentenced Atkins to death. Ibid .; id ., at 309 (majority opinion).

This Court held that Atkins's sentence was unconstitutional 'cruel and unusual punishment' under the Eighth Amendment. Id. , at 311, 321. The Court said that the Eighth Amendment prohibits all ''[e]xcessive' sanctions.' Id ., at 311. Whether a punishment was excessive, the Court said, depended not on the 'standards that prevailed . . . when the Bill of Rights was adopted,' but on the ''evolving standards of decency that mark the progress of a maturing society.'' Id ., at 311–312 (quoting Trop v. Dulles , 356 U. S. 86, 100–101 (1958)). According to the Court, “the American public, legislators, scholars, and judges ha[d] deliberated” over whether “the death penalty should ever be imposed on a mentally retarded criminal' and decided that it should not. Atkins , 536 U. S., at 307, 313-317. The Court concluded that there was a 'national consensus' against imposing the death penalty on the mentally retarded, largely because 18 States barred it. Id ., at 314-316. The Court itself agreed with this supposed 'consensus'; it was 'not persuaded that the execution of mentally retarded criminals will measurably advance the deterrent or the retributive purpose of the death penalty.” Id ., at 321.

The Atkins Court promised that it would allow States to define mental retardation. It admitted that there was 'serious disagreement' about 'determining which offenders are in fact retarded.” Id ., at 317. Accordingly, the CourtPage 28 decided to ''leave to the State[s] the task of developing appropriate ways to enforce the constitutional restriction upon [their] execution of sentences.'' Ibid . So, despite the Court's holding that the Eighth Amendment forbids 'the execution of mentally retarded offenders,' whether an offender was 'mentally retarded' would depend on state rules. Ibid .

Still, the Court suggested that someone with an IQ above 70 could not be mentally retarded for Eighth Amendment purposes. See id. , at 308, n. 3, 316-318; Brumfield v. Cain , 576 U. S. 305, 345-346 (2015) (THOMAS, J., dissenting). The Court drew from 'clinical definitions of mental retardation' that include three necessary elements. Atkins , 536 U. S., at 318. First, the offender must have ''subaverage intellectual functioning'' based primarily on IQ tests. Id ., at 308, n. 3, 318. Second, he must have 'significant limitations in adaptive skills such as communication, self-care, and self-direction.” Id ., at 318. And third, these limitations must have manifested before age 18. Ibid . ''Mild' mental retardation,' the Court explained, 'is typically used to describe people with an IQ level of 50–55 to approximately 70.” Id ., at 308, n. 3. Apparently drawing on that category's upper limit, the Court noted that 'only five [States] ha[d] executed offenders possessing a known IQ less than 70 since” 1989. Id ., at 316. It was thereafter reasonable to understand Atkins to allow States to execute people with IQs above 70. See Brumfield , 576 U. S., at 345-346 ( ).

In the years since, the Alabama courts have faithfully applied that understanding of Atkins . When called to implement it, they observed that other 'states with statutes prohibiting the execution of a mentally retarded defendant require that a defendant, to be considered mentally retarded, must have significantly subaverage intellectualPage 29 functioning (an IQ of 70 or below), and significant or substantial deficits in adaptive behavior” “before the defendant reached age 18.' Ex parte Perkins , 851 So. 2d 453, 456 (Ala. 2002); see also Ex parte Smith , 213 So. 3d 214, 224 (Ala. 2003). Consistent with Atkins , the Alabama courts held that “[a]ll three factors must be met in order for a person to be classified as mentally retarded for purposes of an Atkins claim.” Smith v. State , 213 So. 3d 239, 248 (Ala. 2007). And, consistent with Atkins , they held that the prisoner has the burden to prove that he is mentally retarded by a preponderance of the evidence. 213 So. 3d, at 252.

When it came to applying Atkins to Smith, the Alabama courts had no trouble recognizing that he did not satisfy the first requirement and therefore is not mentally retarded. The Court of Criminal Appeals explained that, by 2008, Smith had scored 75, 74, and 72 on three IQ tests. Smith v. State , 71 So. 3d 12, 19-20 (2008). Though his lowest score suggested that Smith’s true IQ “could be . . . as low as 69” taking account of the error range for that score, it could also be “as high as 75.” Id ., at 19. Smith asked the court 'to apply that margin of error to conclude that . . . he is mentally retarded.” Id ., at 20. But the court rejected that argument, which would require “expanding the definition of mentally retarded' to include people whose true IQ is likely above 70. Ibid .

Unable to persuade the Alabama courts that he was mentally retarded, Smith sought habeas relief in federal court, arguing that the Alabama courts unreasonably applied Atkins . See 28 U. S. C. §2254(d). The District Court initially denied habeas relief for the straightforward reason that the Court of Criminal Appeals did not act unreasonably when it refused to “reduc[e]” Smith’s lowest “IQ score of 72 such that [it] would . . . fall within the mental retardation range.” Smith v. Thomas , Civ. Action No. 05-0474 (SD Ala., Sept. 30, 2013), ECF Doc. 59, pp. 61-62. Smith's own expert, the court explained, testified that his scores were at Page 30best close ' 'to those individuals who would be considered mentally retarded''-a conclusion that 'is incompatible with a determination that Smith is mentally retarded himself.” Id ., at 60 (emphasis deleted). And, the court observed, 'every IQ test administered to Smith during his developmental period yielded an unadjusted score above the cutoff for mental retardation.” Id ., at 61, n. 24.

The Eleventh Circuit disagreed. It thought that it was 'unreasonable' to suppose that Smith did not have significantly subaverage intelligence. Smith v. Campbell , 620 Fed. Appx. 734, 750-751 (2015). The court ordered the District Court to give Smith a new hearing for reconsideration of his Atkins claim de novo . 620 Fed. Appx., at 751-752.

Smith would go to his hearing armed with new decisions of this Court. In Hall v. Florida , 572 U. S. 701 (2014), this Court acknowledged that States can require defendants to show an IQ of 70 or below in order to establish that they are mentally retarded, but held that States must in some manner account for the test’s standard error range. States may, “consistently with Atkins ,' define mental retardation to require an IQ of “70 points” or below if they consider “the IQ test's standard error of measurement.' Id ., at 711-712. Under Florida's test, as the Court understood it, a prisoner with a single IQ score of 71 whose error range included 70 would be conclusively not mentally retarded even if “other evidence' suggested that his 'true IQ' was in fact 70 or below. Id ., at 712, 713. The Court thought that this 'strict IQ test score cutoff of 70' was impermissible because it 'ignores the inherent imprecision of ' IQ tests and 'risks executing a person who suffers from intellectual disability.' Id ., at 712–713, 723. Hall therefore held it unconstitutional to treat as decisive a single above-70 score whose error range includes 70. Id ., at 723-724. In imposing this newPage 31 constitutional rule, Hall relied on 'medical experts' and “professional studies.” Id ., at 709–710.

Hall did not tell courts what to do when low scores whose error ranges touch 70 are paired with multiple higher scores whose error ranges do not. The Court, as in Atkins , left States without guidance: “[T]he analysis of multiple IQ scores jointly is a complicated endeavor.' 572 U. S., at 714. Exactly how courts should weigh multiple IQ scores remained unclear. See id ., at 742-743 ( ).

The next two decisions further walked back Atkins ’s promise to allow States to define mental retardation and instead outsourced the project to clinical practice. In Moore v. Texas , 581 U. S.¹ (2017) ( Moore I ), the Court reiterated that “courts must account for” a test’s error range “where an IQ score is close to, but above, 70' because 'other evidence' may show that ''[the] individual's true IQ score'' is 70 or less. Id ., at 13-15. The Court also told lower courts not to “overemphasiz[e] . . . perceived adaptive strengths” when considering whether the prisoner has 'significant adaptive deficits” under the second element of the mentalretardation definition. Id. , at 15-16. And it criticized the use of factors under that element that invite 'lay perceptions of intellectual disability' and 'lay stereotypes' to guide the analysis. Id. , at 18. Then, in a second Moore v. Texas , 586 U. S. 133 (2019) ( per curiam ) ( Moore II ), the Court reaffirmed these additional restrictions. Id. , at 139– 143. The Court in Moore I and Moore II based its conclusions, not on States' actual practices, as in Atkins , but “solely on what it deem[ed] to be medical consensus about intellectual disability.” See Moore I , 581 U. S., at 22, 29 (ROBERTS, C. J., dissenting).

After these decisions, Smith returned to the District Court. Smith v. Dunn , Civ. Action No. 05–00474 (SD Ala., Aug. 17, 2021), ECF Doc. 135. Since the last hearing, Page 32Smith's expert had administered a test on which Smith scored 78, making his claim of mental retardation even more implausible. App. 167, 218. The expert admitted that “78 is definitely above 70 to 75 IQ range” and indicates an IQ as high as 83. Id ., at 167, 218-219. In addition, another test his own expert administered indicated that Smith reads 'at an 11th-grade level'-a result that the expert admitted is “not consistent” with mental retardation. Id ., at 228–229.

In 2017, the State’s expert administered a fifth IQ test on which Smith, again, scored higher than 70. Smith scored a 74. Even in isolation, that score yielded a 90th percentile confidence level that Smith's IQ is 71 to 78. Id ., at 268. The State’s expert also emphasized that Smith “show[ed] up at an 11th-grade level with regard to sentence comprehension,' a fact that is 'totally inconsistent with intellectual disability.” Id ., at 285. Overall, both experts agreed that Smith’s IQ scores over 35 years demonstrated a remarkably consistent pattern. Id ., at 167, 270. The IQ scores before the District Court were 75, 74, 72, 78, and 74.

Nonetheless, the District Court found that Smith is mentally retarded and therefore that his death sentence was unconstitutional. ECF Doc. 135, at 7. The court conceded that Smith's performance on the test the State's expert administered is 'above what is considered significant subaverage intellectual functioning.” Ibid . It further acknowledged that “multiple IQ scores . . . taken over a long period of time place him in the borderline range, functioning just above intellectual disability.' Ibid . The court admitted that “this leans in favor of finding that Smith does not have significant subaverage intellectual functioning.” Ibid . But it still did “not find it strong enough” to not move on to the second step of Alabama's mental-retardation test and address Smith’s “adaptive deficits.” Ibid . The District Court thought that Smith's scores left it 'not clear' whether he was mentally retarded because his lowest score, 72, “ could mean his IQ is actually as low as 69.'Page 33 Id ., at 5, 10 (emphasis added). So the court moved on. Because of Smith's adaptive deficits, the court found that he has significant subaverage intellectual functioning. After concluding that Smith is mentally retarded, the court vacated his death sentence. Id ., at 4-13.

The Eleventh Circuit affirmed. Smith v. Commissioner, Ala. Dept. of Corrections , 67 F. 4th 1335 (2023) ( per curiam ). The court acknowledged that '[w]hether Smith has significantly subaverage intellectual functioning turns on whether he has an IQ equal to or less than 70.” Id ., at 1345 (citing Ex parte Perkins , 851 So. 2d, at 456). Given that Smith had five IQ scores ranging from 72 to 78, one would have thought that this acknowledgment would have resolved the case against Smith. Nevertheless, the court reasoned that 'a district court must move on to consider an offender's adaptive functioning when the lower end of his lowest IQ score is equal to or less than 70,” no matter how many higher test results he has. 67 F. 4th, at 1346; accord, id ., at 1347. In other words, even if Smith had scored four 120s, a single 72 would allow the court to move on to the other mental-retardation factors. 'Smith carried his burden under the intellectual prong,” the court held, because he “needed to prove only that the lower end of his standarderror range is equal to or less than 70.” Id ., at 1349.

When Alabama petitioned this Court for certiorari, we granted the petition and vacated the Eleventh Circuit's judgment. Hamm v. Smith , 604 U. S.¹ (2024) ( per curiam ). The Court asked for clarification about the Eleventh Circuit's reasoning. Id ., at 2. On one reading, the Court thought, the Eleventh Circuit's decision 'would suggest a per se rule that the lower end of the standard-error range for an offender's lowest score is dispositive.' Ibid . Another reading, under which the decision would be more defensible, “would suggest a more holistic approach to multiple IQ scores that considers the relevant evidence.' Ibid . The Page 34Court then invited the Eleventh Circuit to clarify which of those two meanings it intended. Id ., at 2–3.

Taking the hint, the Eleventh Circuit clarified that it meant the more ''holistic approach to multiple IQ scores.'' Smith v. Commissioner, Ala. Dept. of Corrections , 2024 WL 4793028, *1 (Nov. 14, 2024) ( per curiam ). The court, again, upheld the District Court's analysis on the first element because the District Court “found that Smith’s IQ scores could not rule out the possibility that Smith is intellectually disabled.” Id ., at *3 (emphasis added). And, based on that reasoning, the court went on to conclude, not that Smith’s true IQ is likely 70 or lower, but that it “ could be less than or equal to 70.” Ibid . (emphasis added).

This Court, again, granted certiorari. It appeared ready to decide '[w]hether and how courts may consider the cumulative effect of multiple IQ scores in assessing an Atkins claim.' 605 U. S. 1001 (2025).

Today, however, the Court dismisses the State’s petition as improvidently granted, without explanation. The effect of the Court’s failure, twice in this case, to bring clarity to precedents that manifestly “lac[k] clarity” is that Alabama will not be able to carry out its lawful sentence. Moore II , 586 U. S., at 143 (ROBERTS, C. J., concurring).

We should end the hopeless enterprise that this Court today shows it cannot control. Because nothing in the text and history of the Eighth Amendment justifies Atkins , it is demonstrably erroneous. And because we cannot favor decisions lying 'outside the realm of permissible interpretation' 'over the text of the Constitution,' we should overrule Atkins . Gamble v. United States , 587 U. S. 678, 711-712 (2019) (THOMAS, J., concurring). Atkins also cannot survive this Court’s more recent stare decisis criteria because it is egregiously wrong, unworkable, and has created no legitimate reliance interests.

Page 35A

Atkins is demonstrably erroneous. It is irreconcilable with the Eighth Amendment's original meaning, and nothing in the common law supports it.

1

The Eighth Amendment prohibits 'cruel and unusual punishments.” As originally understood, that prohibition concerns cruel and unusual methods of punishment. Grants Pass v. Johnson , 603 U. S. 520, 541-543 (2024); accord, Aldridge v. Commonwealth , 2 Va. Cas. 447, 449-450 (1824) ('merely applicable to the modes of punishment'). Because capital punishment need not be cruel and has not “long fallen out of use,” the “Constitution allows” it. Bucklew v. Precythe , 587 U. S. 119, 129–130 (2019).

The concept of 'cruel' punishments originally meant what it usually means now: 'savage' or 'barbarous' punishments that “give pain to others, in body or mind.” N. Webster, An American Dictionary of the English Language (1828). Thus, punishments like crucifixion or immolation are “cruel,” but death, by itself, is not. See In re Kemmler , 136 U. S. 436, 446 (1890). In England, capital punishment generally consisted in “being hanged by the neck till dead,” 4 W. Blackstone, Commentaries on the Laws of England 370 (1769) (Blackstone), a method that often involved no pain if performed as intended, S. Banner, The Death Penalty: An American History 170 (2002). But for especially 'atrocious crimes' such as high treason, English law contemplated enhanced punishments, including “embowelling alive, beheading, and quartering.'⁴ Blackstone 370. The cruelty of such punishments consisted in the intentional 'superadd[ition]' of 'terror, pain, or disgrace' to death. Ibid . By the founding, these enhanced death sentences were theoretically still authorized, but they had ''dwindled away’ and would for that reason have been ‘unusual’ in the sense that they were no longer 'regularly or customarily Page 36employed.'' Baze v. Rees , 553 U. S. 35, 97 (2008) (THOMAS, J., concurring in judgment).

Supporters of the Eighth Amendment were concerned that Congress, like Parliament before it, might enhance punishments with cruelty that had by the founding fallen into disuse. See id. , at 97-98. One speaker at the Massachusetts ratifying convention complained that the original Constitution 'nowhere restrained' Congress 'from inventing the most cruel and unheard-of punishments,” leaving “ racks and gibbets ” as “amongst the most mild instruments of their discipline.² Debates on the Constitution 111 (J. Elliot ed., 2d ed. 1891). And Patrick Henry complained that, without a Bill of Rights, Congress could inflict 'tortures, or cruel and barbarous punishment[s].” 3 id ., at 447– 448.

Atkins claims, including Smith's, have nothing to do with these concerns. Executing someone with a particular IQ does not implicate a 'method' of execution at all. It certainly does not implicate a method that rises to the level of deliberate and unusual torture. It is therefore beyond the scope of the Eighth Amendment.

The only possible historical analogue to Atkins 's doctrine was a common-law protection that cannot justify it. At common law, the severely mentally retarded-whom the common law called “idiots”—could not be punished.⁴ Blackstone 24–25. The common law protected such people from punishment because their disability is so severe that they lack 'knowledge to distinguish between good and evil''[t]hey are forgiven for they know not what they do!' A. Highmore, Law of Idiocy and Lunacy 195 (1807) (Highmore). Idiots, said Hale, have 'no possibility to understand, what is forbidden by law to be done, or under what penalties.'¹ M. Hale, Pleas of the Crown 34 (1736) (Hale).

Page 37In modern parlance, one had to be 'severely' or 'profoundly' mentally retarded to be a common-law idiot. Penry , 492 U. S., at 333. Psychiatrists recognize 'four degrees of mental retardation: mild, moderate, severe, and profound.” Smith , 213 So. 3d, at 248-249, and n. 3. ''Mild' mental retardation,” Atkins explained, “is typically used to describe people with an IQ level of 50–55 to approximately 70.” 536 U. S., at 308, n. 3. People within this category 'know the difference between right and wrong and are competent to stand trial.” Id. , at 318. 'Moderate' describes those whose IQs are 35–40 to 50–55. Smith , 213 So. 3d, at 249, n. 3. 'Severe' describes those whose IQs are 20-25 to 35–40. Ibid . And 'profound' describes those whose IQs are below 20 or 25. Ibid . This Court has explained that common-law idiots generally had IQs around 25, making them severely or profoundly mentally retarded. See Penry , 492 U. S., at 333.

The common law therefore provides no support for Atkins claims, as this case demonstrates. No one contends that Smith is a common-law idiot. He reads at an 11th-grade level. His IQ is above 70-above the threshold for mental retardation and about triple what is typical of idiots. And, even setting aside IQ entirely, there is no doubt that Smith is able 'to distinguish between good and evil,' Highmore 195, and that he is able to 'understand . . . what is forbidden by law,'¹ Hale 34. His own expert 'found that . . . Smith knew right from wrong.' ECF Doc. 135, at 3.

* * *

Nothing in our history, from 1791 to 2002, suggests that there is anything unlawful about executing murderers now protected by Atkins —let alone one such as Smith who reads at an 11th-grade level and has never scored below 71 on a single IQ test. We therefore must adhere 'to the correct, original meaning' of the Eighth Amendment, not Atkins . Gamble , 587 U. S., at 712 (THOMAS, J., concurring).

Even under its modern approach to stare decisis , this Court has ''often'' concluded that precedents must be overruled. Ramos v. Louisiana , 590 U. S. 83, 116-122 (2020) (KAVANAUGH, J., concurring in part). Atkins satisfies the criteria the Court has recently relied on to overrule constitutional precedents. See Ramos , 590 U. S., at 120–122.

Atkins is egregiously wrong, unworkable, and has created no legitimate reliance interests. Ramos , 590 U. S., at 121– 122. Atkins is egregiously wrong because it is irreconcilable with original meaning and was poorly reasoned from the start, as more recent Eighth Amendment precedents discrediting its methodology show.* See Part II-A, supra ; Atkins , 536 U. S., at 321-328 (Rehnquist, C. J., dissenting); id ., at 337-354 (Scalia, J., dissenting). Atkins is also unworkable, as its progeny and this case demonstrate. See Part I, supra . Finally, prospective murderers who would argue that they are too unintelligent to be executed are not planning murders in 'reliance' on this Court's Eighth Amendment jurisprudence. Ramos , 590 U. S., at 122 (opinion of KAVANAUGH, J.). Nor, if they were, would such a reliance interest be “legitimate.” Ibid . Stare decisis is therefore no obstacle to restoring the original meaning of the Eighth Amendment. See, e . g ., Dobbs v. Jackson Women’s Health Organization , 597 U. S. 215, 263-290 (2022); Ramos , 590 U. S., at 105–109.

Page 39“Some of our most ‘egregious’ cases have been those in which we have granted relief based on an unfounded Eighth Amendment claim,” and Atkins is certainly near the top of the list. Glossip v. Gross , 576 U. S. 863, 905-906 (2015) (THOMAS, J., concurring). Atkins 's rejection of 'the historical meaning of the [Eighth] Amendmen[t],' see Ramos , 590 U. S., at 106, has denied the justice governments have given to murder victims from time immemorial, Glossip , 576 U. S., at 905-906 (THOMAS, J., concurring). And it degrades the mildly intellectually disabled by putting them 'on a level with . . . infants, imbeciles, and domestic animals'-those who cannot ''have known better.'' C. S. Lewis, The Humanitarian Theory of Punishment, 13 Issues in Religion and Psychotherapy 147, 151 (1987); see Atkins , 536 U. S., at 318, 319-320. In a future case, the Court should overrule Atkins and restore “the Cruel and Unusual Punishments Clause's fixed meaning in resolving any challenge brought under it.' Grants Pass , 603 U. S., at 562 (THOMAS, J., concurring). For now, I respectfully dissent.

Page 40SUPREME COURT OF THE UNITED STATES

No. 24-872

ON WRIT OF CERTIORARI TO THE UNITED STATES COURT OF APPEALS FOR THE ELEVENTH CIRCUIT

[May 21, 2026]

JUSTICE ALITO, with whom JUSTICE THOMAS joins, and with whom THE CHIEF JUSTICE and JUSTICE GORSUCH join as to Parts I, III, and IV, dissenting.

In Atkins v. Virginia , 536 U. S. 304 (2002), this Court held that the Eighth Amendment forbids the execution of defendants whom it described, using the standard terminology of the time, as “mentally retarded.” Atkins did not define that term for Eighth Amendment purposes, and our subsequent decisions on the issue have spawned doctrinal ambiguity and numerous unanswered questions. See, e . g ., Hall v. Florida , 572 U. S. 701, 740-742 (2014) ( ); Moore v. Texas , 581 U. S. 1, 28-33 (2017) (ROBERTS, C. J., dissenting); Bowling v. Commonwealth , 163 S. W. 3d 361, 369, 375 (Ky. 2005) (enumerating several basic questions that Atkins generated but left unresolved).

This case presents one of those questions: How should a court apply a 70-IQ cutoff when a defendant has multiple test scores in the record? As the decisions below demonstrate, our failure to address this recurring question has led to confusion and unsound analysis in lower courts. When the Court granted Alabama's most recent petition in this case, we asked the parties and amici to brief this question. 605 U. S. 1001 (2025). Their briefing provided helpful insight on analyzing multiple scores cumulatively. The CourtPage 41 nonetheless dismisses this opportunity to provide muchneeded guidance to lower courts, even though six Justices stake out a position on whether the decision below is correct. See ante, at 13 (SOTOMAYOR, J., joined by JACKSON, J., concurring).

I respectfully dissent from the Court’s decision to leave this important question unanswered. At the very least, we should reverse the lower courts' erroneous analysis of Smith’s scores and remand for a fresh consideration of his Atkins claim using any sound method. Even if our decision went no further, we would provide clarity and coherence to one aspect of our Atkins doctrine. Instead, the Court shies away from its obligation to provide workable rules for capital cases. In doing so, the Court disserves its own deathpenalty jurisprudence, States' criminal-justice systems, lower courts, and victims of horrific murders.

I write to clarify the scope of our decisions in Hall and Moore , offer guidance on how courts may evaluate multiple IQ scores, and explain how the lower courts’ decisions in this case contravened psychology, statistics, and precedent.

Before Atkins , a defendant convicted of a capital offense could argue at the sentencing phase of his trial that the death penalty should not be imposed because his “mental retardation'-a condition that psychologists now term 'intellectual disability”—diminished his culpability. Bobby v. Bies , 556 U. S. 825, 827-828 (2009). Specifically, under Penry v. Lynaugh , 492 U. S. 302 (1989), a defendant could argue that his disability rendered him 'less able than a normal adult' to 'act 'deliberately,'' 'control his impulses,' or 'evaluate the consequences of his conduct.' Id ., at 322–328. Applying this regime, Virginia sentenced Daryl Atkins to death after he unsuccessfully attempted to mitigate his culpability using evidence of intellectual disability.

Page 42When Atkins's case made it to this Court, he contended that Penry 's individualized approach was insufficient to protect nonculpable defendants under the Eighth Amendment. In particular, Atkins argued that juries could not make 'reliable sorting decisions among defendants with mental retardation” and had not “cull[ed] the more culpable from those whose disabilities [should] preclude' a death sentence. Brief for Petitioner in Atkins v. Virginia , O. T. 2001, No. 00-8452, p. 39. Atkins therefore urged the Court to replace Penry 's 'case-by-case administration' with a 'categorical rule' barring imposition of the death penalty on any 'perso[n] with mental retardation.' Brief for Petitioner in No. 00-8452, at 39-40. The Court ultimately agreed with Atkins, holding that 'the execution of mentally retarded criminals” violates the Eighth Amendment. Atkins , 536 U. S., at 321.

One might have expected that the Atkins Court, in imposing a new categorical rule, would have also defined the category in question. Yet Atkins did not. Id ., at 317. That void entailed two consequences. First, States and lower courts would need to develop their own categorical definitions that were susceptible of judicial administration. Ibid. Second, because '[i]ntelligence, as measured by IQ, has predominated as the primary criterion for diagnosing' intellectual disability, it followed that IQ would feature in these definitions and play a central role in adjudicating Atkins claims. American Association on Mental Retardation, Mental Retardation: Definition, Classification, and Systems of Supports 25 (10th ed. 2002) (AAMR); see, e . g ., id ., at 21–23 (cataloging the consistent use of an 'IQ Cutoff ' as a diagnostic requirement in the five decades leading up to Atkins ); AAMR 66 (noting that possessing an IQ that is two or more standard deviations below the mean is a 'necessary . . . criterion to establish a diagnosis of mental retardation'); American Psychiatric Association, Diagnostic and Statistical Manual of Mental Disorders 41 (rev. 4th ed. 2000) ('ThePage 43 essential feature of Mental Retardation” is an “IQ of about 70 or below”).

In the years since Atkins, IQ has remained a central component of intellectual-disability diagnoses and Atkins claims. On the diagnostic end, '[i]dentifying deficits in intellectual functioning via IQs” continues to be “the standard of practice, as it has been for approximately a century.” R. Floyd, R. Farmer, W. Schneider, & K. McGrew, Theories and Measurement of Intelligence, in 1 APA Handbook of Intellectual and Developmental Disabilities 392 (L. Glidden ed. 2021) (APA Handbook). Likewise, governments continue to incorporate IQ thresholds into intellectual-disability definitions that determine a defendant's eligibility for the death penalty. See, e . g ., Ex parte Perkins , 851 So. 2d 453, 456 (Ala. 2002); Ky. Rev. Stat. Ann. §532.130(2) (West Cum. Supp. 2025).

Initially, Atkins entrusted States with the task of developing judicially manageable criteria to define intellectual disability and assess a defendant’s IQ. 536 U. S., at 317; Bies , 556 U. S., at 831. In the ensuing years, however, this Court has inserted itself into that role and constitutionalized various rules for evaluating intellectual disability. Three of these rules concern IQ cutoffs and test scores.

First, in Hall , the Court clarified that States may use a 70-IQ cutoff for Atkins claims. Hall concerned a Florida statute that defined “intellectual disability” as an IQ of 70 or less and “deficits in adaptive behavior” that manifested before age 18. Fla. Stat. §921.137(1) (2013); Hall , 572 U. S., at 711. Addressing this provision, this Court concluded:

'On its face this statute could be interpreted consistently with Atkins and with the conclusions this Court reaches in the instant case. Nothing in the statute precludes Florida from taking into account the IQ test’s standard error of measurement, and as discussed below there is evidence that Florida’s Legislature

Page 44intended to include the measurement error in the calculation.” Id ., at 711–712.

The undeniable thrust of this analysis is that a 70-IQ cutoff is constitutional, provided that courts consider measurement error when applying it. If that were not so-if a 70IQ cutoff could never be dispositive of an Atkins claim—then Hall could not have held that Florida's statute was 'consisten[t] with Atkins .” 572 U. S., at 711. Hall thus clarified that the Eighth Amendment does not bar the death penalty when a defendant fails to prove that his IQ is 70 or below. This conclusion cohered with Atkins , which keyed its holding to a purported “national consensus” against “execut[ing] offenders possessing a known IQ less than 70.' 536 U. S., at 316.

While Hall affirmed a 70-IQ cutoff for Atkins claims, it imposed a constitutional rule about how courts may apply that cutoff to an IQ test score. At the time of Hall , Florida treated a test score as a 'final and conclusive' determination of a defendant’s IQ and “refus[ed]” to consider possible measurement error. 572 U. S., at 712. Thus, if a defendant failed to produce a test score of 70 or below, Florida courts rejected Atkins relief without considering any other evidence. Hall rejected Florida's approach. Although Hall acknowledged that sufficiently high scores might be dispositive in some cases, 572 U. S., at 715, the Court held that courts must account for a test's 'standard error of measurement,” an estimate of the test’s possible error, id ., at 723– 724. To do so, courts must interpret an individual test score using a “confidence interval” that captures a range of IQs, rather than as a single point estimate.¹ If the confidencePage 45 interval for a score spans 70 or lower, courts may not treat that score as singly dispositive of an Atkins claim. 572 U. S., at 723.

Three years later in Moore , this Court announced another constitutional rule of IQ analysis. There, a Texas defendant obtained a test score of 74 with a corresponding confidence interval spanning 69 to 79. 581 U. S., at 10. In determining whether the defendant satisfied a 70-IQ cutoff, the Texas Court of Criminal Appeals considered factors beyond the test score and its standard error of measurement. For example, the court noted that the defendant had possibly experienced depression when he took the IQ test. Ex parte Moore , 470 S. W. 3d 481, 517-519 (2015). The court also recognized that he had 'external motivations to obtain a lower score, such as facing the death penalty” if he scored too high. Id ., at 517. Based on these extrinsic details, the Texas court concluded that there was “no reason to doubt” that the defendant’s “actual IQ” was in the “higher portion” of the 69-to-79 interval and thus above 70. Id ., at 519. The court accordingly denied Atkins relief on IQ grounds.

Moore rejected this analysis, holding that courts may not rely on “factors unique to [the defendant]” to conclude that his 'true' IQ falls in one range of a confidence interval rather than another. 581 U. S., at 14. Put differently, Moore held that courts may not inflate or deflate estimates of a defendant's IQ based on specific details about him. When determining a defendant’s IQ, a court must consider only his test scores and valid statistical analysis.

Page 46Our case law has thus laid out three rules concerning IQ and Atkins claims. First, Atkins does not bar the execution of a defendant who fails to prove an IQ of 70 or lower. Second, when determining whether a defendant has met this 70-IQ threshold, a court may not treat any one score as dispositive without considering a confidence interval based on the test's standard error of measurement. And third, courts may not use extrinsic, defendant-specific details to infer where his IQ falls within a given interval.

Although Hall and Moore announced rules about treating a single test score as dispositive, this Court has never explained when courts may treat multiple scores as cumulatively dispositive. Hamm v. Smith , 604 U. S. 1, 2 (2024) ( per curiam ). Our silence on this issue leaves courts without direction on how to address a recurring situation. Because defendants raising Atkins claims have usually taken multiple IQ tests, courts must often apply a 70-IQ cutoff to a defendant with several scores. See, e . g ., Smith v. Ryan , 813 F. 3d 1175, 1183–1184 (CA9 2016) (five scores); State v. Escalante-Orozco , 241 Ariz. 254, 290, 386 P. 3d 798, 834 (2017) (four scores); Black v. Carpenter , 866 F. 3d 734, 737– 738 (CA6 2017) (10 scores); Jackson v. Payne , 9 F. 4th 646, 653 (CA8 2021) (four scores). See also Pet. for Cert. in Saldano v. Texas , O. T. 2025, No. 25-5749, p. 6 (four scores). By Smith's count, Atkins claims presenting multiple IQ scores have arisen at least 56 times since our decision in Hall . See Brief for Respondent 9, and n. 1; App. to Brief for Appellant 1a-17a. These cases 'starkly underscor[e] the need for clarity' on this issue, and our failure to provide it has not gone unnoticed. Busby v. Guerrero , 2026 WL 1291044, *1 (CA5, May 8, 2026) (opinion of Higginson, J.). “In a matter of life and death,” lower-court judges “must be certain that [they] apply the proper constitutional rule.' Ibid.

Page 47Fortunately, psychometric literature provides various methods for estimating a person’s “true” IQ using multiple scores.² Although the Constitution does not require courts to adopt any one approach, the medical community's IQestimation techniques inform our Atkins jurisprudence. Hall , 572 U. S., at 710-713. Thus, courts and legislatures may rely on any reasonably sound method of estimating a defendant's 'true' IQ. The parties and amici discuss several approaches, and I highlight three that appear in the APA's Handbook of Intellectual and Developmental Disabilities.

First, multiple IQ scores may be used to calculate a 'composite score.' This approach provides a mathematically rigorous way to aggregate scores across different tests into a single, more precise estimate. APA Handbook 415-417. Indeed, a prominent psychology expert whom this Court cited in Hall suggests that the composite-score method is appropriate for estimating the “true” IQ of someone “facing the death penalty.” W. Schneider, Can’t Decide Which IQ Is Best? Make a Composite Score 1 (Jan. 13, 2012), http://assessingpysche.wordpress.com/2021/01/13/cantdecide-which-iq-is-best-make-a-composite-iq-score/; accord, D. Watson, Intelligence Testing, in The Death Penalty and Intellectual Disability 124 (E. Polloway ed. 2015) (Watson) (discussing the composite-score approach as an appropriate method in the death-penalty context).

The estimate produced by a composite-score calculation can be interpreted like any other IQ score. In other words, Page 48a composite-score estimate of 70 reflects intellectual functioning that is 'significantly subaverage.' See Schneider, Oxford Handbook 290-291. And because using multiple scores can increase measurement precision, the standard error for a composite score will often be smaller than that for any constituent test score. Id ., at 291; APA Handbook 415-417. The resulting confidence interval for a composite score will thus be narrower. Id ., at 417.

Computing a composite score and its associated standard error of measurement is a multistep calculation that requires the defendant to provide certain statistics about the tests that he has taken. Id ., at 416-417; Watson 124. When a defendant provides all these data, courts, with the assistance of expert witnesses, can construct a composite score and its corresponding confidence interval. Unless that interval spans 70 or below, courts may deny Atkins relief.

Second, if a defendant fails to provide the information necessary to compute a composite score, the 'next best practice' for estimating someone's 'true' IQ is to take the median value of his scores. Watson 124. The median score is a 'reasonable estimate' of a defendant's 'true' IQ that is 'appropriate and useful' where the 95% confidence intervals for all an individual’s scores overlap. APA Handbook 415. Thus, when this condition is met, courts adjudicating Atkins claims can 'reasonabl[y]' and 'appropriate[ly]' conclude that a defendant's IQ is above 70 when his median score exceeds 70. APA Handbook 415.

Third, some have suggested that it may be valid for an expert witness to take a less formal approach and make a judgment call about the “central tendency” of a defendant’s various scores. Ibid . When a defendant takes multiple tests, his scores will usually “cluster” around his “true” IQ. A. Frances, Essentials of Psychiatric Diagnosis: Responding to the Challenge of DSM-5, pp. 30-31 (2013) (Frances). Under this approach, when an expert determines that a defendant's scores 'cluster,' or evince a 'central tendency,'Page 49 above 70, a court can reasonably conclude that a defendant’s “true” IQ exceeds 70.

Any one of these approaches provides a reasonable way to evaluate whether a defendant’s IQ is 70 or below in Atkins cases involving multiple scores. And when a court using a reasonable method concludes that a defendant’s “true” IQ is above 70, it may reject an Atkins claim solely on that ground.

The courts below did not apply any defensible method to determine Smith's IQ. To the contrary, they relied on psychologically, statistically, and legally unsound analyses to conclude that Smith’s IQ is 70 or below. At the very least, we should reverse and remand to give the lower courts an opportunity to perform a proper analysis.

Consider first the Eleventh Circuit's 2023 decision, which affirmed that Smith was entitled to Atkins relief. The Eleventh Circuit's analysis started off on the right foot. It explained that Smith “ha[d] the burden of proving” that he possessed 'significant subaverage intellectual functioning.' Smith v. Commissioner , 67 F. 4th 1335, 1345 (2023) ( per curiam ) (internal quotation marks omitted). Likewise, the court correctly recognized that '[w]hether Smith has significantly subaverage intellectual functioning turns on whether he has an IQ equal to or less than 70.” Ibid . Thus, in upholding the lower court’s decision to grant Smith Atkins relief, the Eleventh Circuit necessarily concluded that his “true” IQ was 70 or lower.

In reaching this conclusion, however, the Eleventh Circuit employed an illegitimate approach to analyzing Smith’s scores. The record below contained five valid IQ scores for Smith: 75, 74, 72, 78, and 74. 67 F. 4th, at 1345– 1346. When assessing whether Smith's IQ was 70 or lower Page 50based on these data, the Eleventh Circuit did not employ any recognized method for analyzing multiple test scores. Instead, it determined Smith’s “true” IQ by taking the value at 'the lower end' of the confidence interval for 'his lowest IQ score.” Id ., at 1346. Here, Smith's lowest valid score was 72, with a standard error of measurement of 3. Id ., at 1340. From those values, the Eleventh Circuit determined that Smith’s IQ was “actually as low as 69” and his Atkins claim therefore met the 70-IQ cutoff. 67 F. 4th, at 1349. In other words, under the Eleventh Circuit's view, whenever the lower bound of a defendant’s lowest score spans 70 or lower, his Atkins claim satisfies the IQ threshold, and courts must 'move on' to consider evidence for other Atkins criteria. 67 F. 4th, at 1347.

This approach is flagrantly unsound. When a defendant has multiple IQ scores, it is indefensible to use the lower bound of his lowest score to determine whether his 'true' IQ is 70 or below. Such an approach contravenes basic principles of psychological measurement and statistics.

First, psychometric literature teaches that when an individual has multiple IQ scores, the “higher scores are likely to be more indicative' of a person's intelligence than the lower scores. Frances 31; accord, S. Whitaker, The Stability of IQ in People With Low Intellectual Ability: An Analysis of the Literature, 46 Intellectual and Developmental Disabilities, No. 2, p. 126 (2008) (Whitaker) (noting it is 'likely that the higher result [is] the more accurate'). This asymmetry reflects the fact that the possible sources of error in an individual's IQ-test performance, such as uncooperativeness, anxiety, sleep deprivation, malingering, or other mental-health disorders, “will tend to reduce” one’s score. Ibid . In contrast, there is 'no reason why' an IQ score would overestimate someone's intelligence. Frances 31. This principle counsels against making decisions based on someone’s lowest score.

Page 51The Eleventh Circuit flipped this principle of psychology on its head by giving dispositive weight to Smith’s lowest score, which was likely 'subject to more error' and 'less accurate” than the others. Whitaker 126. If anything, the Eleventh Circuit should have given greater weight to Smith’s higher scores of 75 and 78, which indicate that Atkins does not bar his execution. See Hall , 572 U. S., at 715 (noting that the defendant conceded the validity of a brightline 75-IQ cutoff for Atkins claims).

Second—and most critically—the Eleventh Circuit’s sole reliance on the lower bound of Smith's lowest score reflects a basic misunderstanding of statistics. When clinicians construct a confidence interval using the standard error of measurement, their calculations rely on the assumption that a defendant's test scores are normally distributed around his “true” IQ— i . e ., if a defendant took a large number of IQ tests, the scores would form a bell curve centered on his 'true' IQ. Cohen 176; K. Widaman, Concepts of Measurement, in The Death Penalty and Intellectual Disability 68 (E. Polloway ed. 2015). Under that assumption, an individual’s score on any given test is more likely to be close to his 'true' IQ than far away from it. This fact, in turn, means that the values near the center of a confidence interval are more likely estimates of the defendant’s “true” IQ than the values at the interval’s upper and lower bounds. See G. Cumming & F. Fidler, Confidence Intervals Give Better Answers, 217 J. Psychology 18 (2009); G. Cumming, Inference by Eye: Pictures of Confidence Intervals and Thinking About Levels of Confidence, 29 Teaching Statistics 90–91 (2007).

The Eleventh Circuit’s analysis ignored this attribute of confidence intervals. It concluded that Smith's IQ was 70 or below because the lower bound of the interval for one score was 69. But the fact that 69 marked the lower limit of the interval meant that this value was less likely to reflect Smith's 'true' IQ than other, higher values in the Page 52interval. Once again, the Eleventh Circuit's analysis was precisely backward.

The Eleventh Circuit attempted to justify its approach by citing Hall and Moore . On its reading of those cases, any time that the lower bound of a defendant's lowest score descends to 70 or below, IQ cannot be dispositive, and courts must decide an Atkins claim based on evidence of the defendant's adaptive functioning. 67 F. 4th, at 1348-1349 (“ Hall and Moore required the district court to turn to evidence of Smith’s adaptive deficits because the lower end of his standard-error range was 69”). But as we recognized the last time that this case was before us, neither Hall nor Moore established any rules for analyzing multiple IQ scores, much less the one-low-score approach that the Eleventh Circuit took. Hamm , 604 U. S., at 2 (“This Court has not specified how courts should evaluate multiple IQ scores” (citing Hall , 572 U. S., at 714, and Moore , 581 U. S., at 1)).

Start with Hall . To be sure, the defendant in that case had taken multiple IQ tests. 572 U. S., at 707. But neither the Florida courts nor this Court considered the cumulative significance of his scores. See Hall v. State , 109 So. 3d 704, 707–711 (Fla. 2012) ( per curiam ); Hall , 572 U. S., at 724. Under then-controlling Florida case law, state courts considered each score individually. See Cherry v. State , 959 So. 2d 702, 712-714 (Fla. 2007). Unless a defendant provided at least one score of 70 or below, Florida courts would deny relief. Although Hall rejected this approach, the decision did not explain how courts should consider the cumulative significance of multiple scores. To the extent that Hall addressed multiple-score analysis at all, it held only that courts must 'take into account' potential measurement error. 572 U. S., at 724. Hall did not, however, explain how to account for error across multiple scores. It merely noted that such analysis is a 'complicated endeavor,” one that neither Florida courts nor this Court had Page 53undertaken. Id ., at 714. This cursory discussion is hardly the sort of treatment that the Court would have given if it had intended to impose a one-low-score approach.³

Moore did not mandate the Eleventh Circuit's approach, either. As I have already explained, Moore prohibited courts from using extrinsic facts about a defendant to draw conclusions about where his 'true' IQ falls within a confidence interval. Beyond that, Moore ’s IQ discussion merely reaffirmed Hall 's holding that courts must consider the standard error of measurement when applying a 70-IQ cutoff to a single score. 581 U. S., at 14. Moore did not articulate any rules about analyzing multiple scores in aggregate. As in Hall , the defendant in Moore had multiple IQ scores in the record, id ., at 10, but neither the Texas court nor this Court considered those scores collectively, see Ex parte Moore , 470 S. W. 3d, at 519; Moore , 581 U. S., at 14.

If psychology, statistics, and our case law do not suffice to underscore the flaws of the Eleventh Circuit's one-lowscore approach, common sense seals the deal. The Eleventh Circuit's approach would produce absurd results. Imagine that a defendant had taken an IQ test every year from first grade through high-school graduation. Suppose that five of these scores were 100, five were in the 90s, one was in the 80s, and one was 71 on a test with a standard error of 3. On this hypothetical record, there would be no practical likelihood that the defendant’s IQ is 70 or below. Rather, the most reasonable conclusion would be that the 71 score is an outlier, and that its confidence interval does not capture the defendant's 'true' IQ. But under the Eleventh Circuit's Page 54one-low-score rule, a court could not deny Atkins relief on these scores unless it separately found inadequate the defendant's adaptive-functioning evidence. In effect, a court would need to ignore the defendant’s 11 higher scores and consider only the outlier. That approach cannot be correct, and our case law does not command it.

In short, the Eleventh Circuit's 2023 analysis was indefensible. In determining whether Smith satisfied a 70-IQ cutoff, the court focused on the lower bound of the confidence interval for Smith’s lowest score—the least plausible region of the interval for what was likely Smith's least accurate score. Because this Court was troubled by this deeply flawed approach, we summarily vacated the Eleventh Circuit’s decision last Term. Hamm , 604 U. S., at 1– 3.

The Eleventh Circuit’s attempt to resuscitate its decision on remand remained flawed. Once again, the Eleventh Circuit began by correctly noting that Atkins requires Smith to prove that “his IQ is 70 or lower.” Smith v. Commissioner , Ala. Dept. of Corrections , No. 21-14519 (Nov. 14, 2024) ( per curiam ), App. to Pet. for Cert. 3a. The court then concluded that 'the record evidence plausibly supports' the finding that 'Smith's true IQ score could be less than or equal to 70.' Id ., at 7a (emphasis added). In support of this conclusion, the Eleventh Circuit quoted the District Court’s analysis:

''Smith did not consistently score so high that the [c]ourt is confident that the lowest score can be thrown out as an outlier or that the standard error for the' other tests, which individually suggest Smith's true IQ may be 70 or lower, 'can be disregarded.'' Id. , at 6a (quoting Smith v. Dunn , Civ. Action No. 05–cv–00474 (SD Ala., Aug. 17, 2021), App. to Pet. for Cert. 70a; emphasis added).

Page 55This analysis cannot justify granting Atkins relief. First, it is not enough for Smith to show that his “true” IQ “could be' or 'may be' 70 or lower. Rather, Smith needed to show that his IQ is 70 or lower. Moreover, even if the District Court definitively concluded that Smith had a 70-or-lower IQ, the court's reasoning could not support such a conclusion. For reasons that I have already discussed, it is unsound to hold that Smith satisfied a 70-IQ threshold simply because the lower limits of the intervals for some scores descended to 70. To obtain relief, Smith needs to prove that his scores cumulatively demonstrate a 'true' IQ of 70 or lower.

Apart from test scores, the Eleventh Circuit’s decision on remand also relied on evidence of Smith's adaptive functioning to conclude that his IQ was 70 or lower. In particular, the Eleventh Circuit pointed to the District Court's conclusion that '[a]though [Smith] has scored above 70 on many of his IQ tests, his adaptive behavior problems are severe enough that his actual functioning is lower.' App. to Pet. for Cert. 61a. In other words, although Smith's scores all exceeded 70, the courts concluded that his “actual” IQ was lower using evidence other than his scores and their standard errors. Ibid .

This line of reasoning is equally untenable, as it commits the same error that the Texas Court of Criminal Appeals made in Moore . Estimates of Smith's IQ spanned the 70s, yet the courts below concluded that Smith's 'actual' IQ more likely fell in the 70-or-lower range of these intervals. App. to Pet. for Cert. 61a. As in Moore , the lower courts grounded this quantitative conclusion on “factors unique to [Smith].” 581 U. S., at 14. Specifically, the District Court deflated its estimate of Smith’s IQ based on details about his social and interpersonal difficulties, his struggles living independently, and his academic underperformance. App. to Pet. for Cert. 61a. As in Moore , however, none of that evidence permits the lower courts to conclude that Smith'sPage 56 “true” IQ is more likely to fall at the lower (or higher) end of an estimated range. 581 U. S., at 14; accord, Whitaker 126 ('Other sources of information' about 'how the individual functions in his/her environment' cannot be 'used quantitatively to reduce margin of error in an IQ score”).

Indeed, the evidence on which lower courts relied to deflate their estimate of Smith's IQ was even less relevant than the evidence that the Texas court considered in Moore . In Moore , the Texas court relied on evidence that plausibly caused a test to underestimate the defendant's IQ, such as his possible depression on test day and his strong incentive to underperform. Ex parte Moore , 470 S. W. 3d, at 517–519. Here, in contrast, the lower courts discounted Smith’s IQ using facts completely unrelated to his testing, such as his failure to maintain a bank account and his difficulties purchasing groceries. App. to Pet. for Cert. 87a. If Moore prohibits courts from using test-day details to inflate an IQ estimate, then surely it prohibits courts from using sundry facts about a defendant's life before prison to deflate an estimate.⁴ Yet this is precisely the evidence on which the courts below relied to conclude that Smith’s IQ was 70 or below.

Because the Eleventh Circuit continued to rely on unsound reasoning, I would reverse and remand its 2024 decision with instructions to reevaluate Smith’s IQ using any sound method.

Page 57Smith's attempts to defend the judgment below are similarly unpersuasive. Smith contends that Hall and Moore require courts to 'consider other evidence of intellectual functioning” whenever “IQ scores alone are inconclusive.” Brief for Respondent 24. But this contention only raises the question of when multiple scores are 'inconclusive' under Atkins . When pressed at oral argument to address this question, Smith’s counsel steadfastly refused to give a clear or consistent answer. At one point, counsel conceded that several sufficiently high IQ test scores could be dispositive even if one score was 71. Tr. of Oral Arg. 104-105. Moments later, however, counsel suggested that any time the confidence interval for a test score falls below 70, courts must consider evidence beyond IQ tests. Id ., at 120. When we asked counsel to clarify when, if ever, test scores alone could be conclusive, he retorted only that Smith was “not in the same time zone” as a defendant for whom scores might be dispositive. Id ., at 116. Obviously, an “I know it when I see it” rule is plainly inappropriate for determining whether to impose the death penalty. 5Page 58 Smith separately argues that the District Court's analysis merely tracked Alabama law, which does not bar consideration of adaptive-functioning evidence even if a defendant fails to produce a 70-or-lower test score. Brief for Respondent 45-46. But whether the District Court correctly granted habeas relief turns on whether Smith's death sentence violated the Constitution, not Alabama law.⁶ See 28 U. S. C. §2254(a). Regardless, Alabama law, like our Atkins doctrine, requires a defendant to prove that his IQ is 70 or below. See Ex parte Perkins , 851 So. 2d, at 456. Smith has thus far failed to do so under any valid method, and he cannot identify a single Alabama case in which a court granted relief after concluding that a defendant’s IQ exceeded 70. See, e . g ., Mulkey v. State , ___ So. 3d ___ (Ala. Crim. App. 2025) (applying a 70 IQ cutoff and denying relief to a defendant who scored 72). The District Court's decision therefore fares no better under Alabama law.

Page 59The lower courts’ IQ analysis was flawed at every stage of this litigation. Because the courts below have yet to provide a sound basis for granting Smith Atkins relief, the Court should reverse the Eleventh Circuit's decision and remand this case for further proceedings.

JUSTICE SOTOMAYOR attempts to justify dismissing this case on the ground that it does not meaningfully present the question on which we granted certiorari. This assertion blinks reality. The question on which we granted certiorari asks how courts should “consider the cumulative effective of multiple IQ scores in assessing an Atkins claim.” 605 U. S. 1001. When the courts below assessed Smith's claim, they evaluated whether his 'multiple IQ scores' were 'consistently . . . so high' as to establish 'that Smith is not intellectually disabled” under Atkins . App. to Pet. for Cert. 70a. Thus, this case plainly presents the question on which we granted certiorari, as well as the intertwined question of whether the courts below properly analyzed Smith's scores when granting him Atkins relief. Contra, ante, at 911 ( ).

JUSTICE SOTOMAYOR nevertheless emphasizes that 'Alabama never argued that the [District Court] must . . . us[e] any particular method (or set of methods) to assess whether an Atkins claimant has proven significantly subaverage intellectual functioning.' Ante, at 9. But it was not Alabama's burden to explain why Smith's IQ scores disqualified him from Atkins relief. Rather, Smith has the burden of proving that his scores establish an IQ of 70 or less using some defensible method. See Hawk v. Olson , 326 U. S. 271, 279 (1945) ('Petitioner carries the burden in a collateral [habeas] attack'). Alabama has consistently maintained that Smith fails to satisfy this burden given his scores. See Respondent’s Post-Hearing Brief in Smith v. Dunn , No. 05–Page 60 cv–00474 (SD Ala.), ECF Doc. 129, pp. 36–46. The District Court held otherwise only by engaging in unsound analysis, and Alabama has objected to that analysis at every stage of the litigation since. See Respondent’s Motion to Alter or Amend the Judgment in Smith, supra , ECF Doc. 136, pp. 3– 7; Brief for Appellant in No. 21–14519 (CA11), ECF Doc. 12, pp. 40–42; Pet. for Cert. in Hamm v. Smith, O. T. 2023, No. 23-167, pp. 10-20; Pet. for Cert. 26-31. Having properly preserved this issue, Alabama could ''make any argument in support'' of its position in this Court, even if it did not present those ''precise arguments'' below. Lebron v. National Railroad Passenger Corporation , 513 U. S. 374, 379 (1995). Indeed, it was particularly appropriate for Alabama to raise arguments about cumulative-score analysis given that we specifically directed the State to do so.⁷ See 605 U. S. 1001. In suggesting that Alabama needed to raise these same exact arguments below, JUSTICE SOTOMAYOR misunderstands basic party-presentation rules and joins the lower courts in improperly shifting the burden to Alabama.

To be sure, I agree with JUSTICE SOTOMAYOR that the decision below was not “trained on” any rigorous multi-score analysis. Ante, at 8. But that shortcoming is precisely why we should reverse the decision below and remand this case for further proceedings.

Today, the Court declines to offer guidance on analyzing multiple IQ scores despite receiving significant briefing on the issue. The Court's failure to resolve this issue will have

——————Page 61 regrettable consequences. Without clear rules for determining when multiple IQ scores are dispositive, nearly every Atkins case will devolve into an amorphous, individualized determination of whether the defendant meets an imprecisely defined notion of 'significantly subaverage intellectual functioning' under which the role of IQ is not clearly articulated. See ante, at 16-20 ( ) (describing that approach as 'holistic'). Such an approach will place our Atkins doctrine out of step with psychology, our death-penalty jurisprudence, and Atkins itself. In the field of psychology, IQ testing remains the standard practice for measuring intellectual functioning, and it is difficult to find a definition of 'significantly subaverage intellectual functioning' that does not center on IQ. See, e . g ., R. Schalock, R. Luckasson, & M. Tasse, Intellectual Disability: Definition, Diagnosis, Classification, and Systems of Supports 29, 130 (12th ed. 2021) (defining the condition as having an IQ two standard deviations below the mean); APA Handbook 392–393.

It is likewise difficult for courts to develop objective, judicially manageable standards for evaluating intelligence that do not turn on IQ. Without clear IQ criteria, Atkins proceedings will be little more than battles of experts, with one side saying that the defendant's intellectual functioning is “significantly subaverage,” and the other saying that it is not. Whether a defendant lives or dies will hinge on which expert a judge finds more credible. Cf. 536 U. S., at 353 (Scalia, J., dissenting) (predicting that Atkins will 'tur[n] the process of capital trial into a game'). Indeed, both the District Court and Eleventh Circuit openly admitted that whether Smith would be executed ''largely [came] down to which expert' the district court 'believed.'' App. to Pet. for Cert. 8a (quoting id ., at 91a; alteration in original); see 67 F. 4th, at 1353.

This unmoored approach to Atkins will produce the very sort of 'arbitrary and unpredictable' outcomes that our Page 62postGregg death-penalty jurisprudence has sought to avoid. California v. Brown , 479 U. S. 538, 541 (1987); see Gregg v. Georgia , 428 U. S. 153 (1976). If Atkins has any prospect of surviving as a workable doctrine, lower courts need ''clear and objective standards' that provide 'specific and detailed guidance'' on how to analyze multiple IQ scores. Godfrey v. Georgia , 446 U. S. 420, 428 (1980) (plurality opinion) (footnote omitted). The Court's refusal to provide such guidance will continue to undermine the intelligibility of this doctrine.

A case-by-case approach without categorical IQ rules also runs contrary to Atkins 's very premise. As I noted at the outset, Atkins rejected Penry 's regime, under which the relationship between a capital defendant's intellectual capability and his culpability would be assessed on an individualized, case-by-case basis. In its place, Atkins adopted a categorical rule under which IQ would necessarily play a central role. For this rule to function in a defensible way, the Court needs to elucidate sound and reputable methods for dealing with multiple IQ scores. If courts relegate the 70-IQ cutoff to a perfunctory formality and the main point of contention in Atkins cases becomes an individualized assessment of a defendant's adaptive functioning, then the Atkins Court's basis for imposing a categorical rule will disintegrate.⁸

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This case presented an opportunity for the Court to explain how courts should evaluate Atkins claims when the defendant has multiple IQ test scores. Nothing in our case law sanctioned the lower courts’ analyses, and we should have used this case to bring clarity to our Atkins doctrine. By instead remaining silent, the Court exacerbates the confusion that plagues our jurisprudence in this area. If this Court continues to shy away from opportunities to provide workable doctrine, we should not be surprised if petitions asking us to overrule Atkins , Hall , and Moore arrive at our doorsteps soon. See, e . g ., Brief for United States as Amicus Curiae 26-32 (asking the Court to overrule Hall and Moore ); Brief for Commonwealth of Kentucky as Amicus Curiae 2 (urging the Court to “engage in a more wholesale rethinking” of Atkins ); ante , p. 1 ( ); cf. Brief for State of Idaho et al. as Amici Curiae 14-17 (urging the Court to 'undercut the 'evolving standards of decency' framework' even though 'no party has asked for . . . Atkins to be overruled” here); Pet. for Cert. in Ohio v. Ford , O. T. 2019, No. 19–1191, pp. 28–30 (asking this Court to replace our current Atkins doctrine with a rule barring the execution of only those who meet the Model Penal Code’s definition of insane).