In the 1986 case McCleskey v. Kemp, Warren McCleskey, a black man convicted of murdering a white police officer in Georgia and sentenced to death, appealed his sentence on the grounds that it was racially biased. His appeal was based on statistical evidence suggesting racial disparities in sentencing (known as the Baldus study), arguing this violated his Eighth Amendment protection against cruel and unusual punishment and Fourteenth Amendment right to equal protection under law. The Supreme Court ruled 5-4 against McCleskey, stating that he failed to prove intentional discrimination in his specific case despite presenting compelling statistics about systemic bias. The court held that unless discriminatory intent could be proven for individual cases, broad statistical patterns were insufficient for overturning sentences or laws; thus upholding Georgia's capital punishment system.

In the dissenting opinion of McCleskey v. Kemp, Justice Brennan argued that the statistical evidence presented by Warren McCleskey demonstrated a significant risk of racial bias influencing Georgia's capital sentencing process. He contended that this was enough to establish a violation of both the Eighth Amendment’s prohibition on cruel and unusual punishment and Fourteenth Amendment’s guarantee of equal protection under law. Brennan criticized the majority for requiring McCleskey to prove intentional discrimination in his specific case, arguing it is unrealistic given how subtly racism operates within society and institutions. Furthermore, he asserted that death penalty inherently lacks reliability due to its irreversible nature; thus any racial disparities should be addressed seriously rather than dismissed as inevitable part of our criminal justice system. Lastly, he warned against complacency towards systemic biases which undermine public confidence in fairness and integrity of judicial processes.