In Allen v. United States (1894), the U.S Supreme Court ruled on a case involving an individual who was charged with murder in Indian Territory, which is now Oklahoma. The defendant, Mr. Allen, argued that he should have been tried by a jury composed of half Native Americans and half white men because the crime occurred in Indian Territory where both populations resided. However, his trial only included white jurors due to federal law at that time stipulating juries were to be drawn from citizens of the state or district where courts were held; since there were no states or districts within Indian Territory then, only federally recognized citizens - whites - could serve as jurors. The court rejected this argument stating that while it might seem unfair not to include Native Americans on juries for crimes committed in their territory, it did not violate any constitutional rights because they weren't considered U.S citizens under existing laws and therefore couldn't serve as jurors according to those same laws. This decision upheld Mr. Allen's conviction and reinforced racial exclusionary practices regarding jury selection during this period.

In the dissenting opinion for Allen v. United States, Justice Brewer argued that the trial court erred in its instructions to the jury regarding reasonable doubt. He contended that by instructing jurors they could find guilt beyond a reasonable doubt even if they believed there was a possibility of innocence, it lowered the standard of proof required for conviction and violated due process rights. Brewer asserted this instruction allowed jurors to convict based on mere probability rather than certainty, which he viewed as contrary to established principles of criminal law requiring guilt be proven beyond a reasonable doubt. He also expressed concern about potential implications for future cases if such an interpretation were permitted.