Final answer:
When the Supreme Court declines to hear a case, the lower court's decision stands as the final judgment. This occurs when a petition for a writ of certiorari is denied, a decision often stemming from the Court's careful selection of impactful and complex legal issues for its limited docket.
Step-by-step explanation:
When the Supreme Court refuses to hear a case, the decision of the lower court remains in effect. The process leading to such a refusal usually involves a petition for a writ of certiorari, where the Court is asked to review the case. However, due to the high number of requests and the Court's discretion to choose cases that have a significant legal question or involve constitutional issues, most petitions are denied.
Each year, the Supreme Court receives thousands of petitions, but hears fewer than one hundred cases. If the Court declines to grant certiorari, which requires the affirmative vote of at least four justices (the Rule of Four), the appellate court's ruling is the final word on that legal dispute. This selectivity enables the Court to focus on cases of national importance or those that address inconsistencies in the interpretation of federal law or the Constitution.