In Downman v. State of Texas, 1913, the U.S. Supreme Court examined a case involving an individual named Downman who was convicted for murder in Texas and sentenced to death by hanging. The main issue under review was whether or not the trial court had erred in refusing to allow evidence that would have shown that one of the jurors held prejudice against people accused of crimes like those committed by Downman. In its decision, the Supreme Court ruled that it did not possess jurisdiction over this matter as there were no federal questions involved; all issues raised pertained solely to state law and procedure which fell outside its purview. Therefore, it dismissed the writ of error filed by Downman's counsel seeking reversal of his conviction on these grounds.

In the dissenting opinion for Downman v. State of Texas, it was argued that the majority's decision violated the defendant's constitutional rights to a fair trial and due process. The dissenting justices believed that there were significant procedural errors in how the case was handled at both the trial and appellate levels, which unfairly prejudiced against Mr. Downman. They contended that these errors included improper jury instructions, exclusion of key defense evidence, and an overly broad interpretation of what constituted "robbery" under Texas law - all contributing to an unjust conviction. Furthermore, they disagreed with how quickly Mr.Downman’s appeal had been dismissed by lower courts without proper consideration given to his claims of error during his initial trial proceedings; thus denying him access to full legal recourse available under law.