Final answer:
The Supreme Court uses a writ of certiorari process to decide on hearing an appeal and considers constitutional questions or differences in law interpretation. The decision-making is influenced by legal, personal, ideological, and political factors, including input from law clerks, the solicitor general, interest groups, and media coverage. They review case briefs and hold private conferences before making a public decision.
Step-by-step explanation:
When the Supreme Court is deciding whether to grant an appeal, it largely relies on a process involving a writ of certiorari. This is a request for judicial review where a lower court is ordered to send its records to the Supreme Court. The Court is selective in granting certiorari; it seeks cases that present constitutional questions or varying interpretations of law. If the request is not granted, the lower court's decision stands. This can occur when the justices feel the case lacks a significant legal question or agree with the lower court's ruling.
Influences on the Supreme Court also play a key role. Among these influences are legal constraints such as facts of the case, the Constitution, existing laws, and judicial precedents. Additionally, personal, ideological, and political views may affect decision-making, despite the aim for impartiality. Law clerks, the solicitor general, interest groups, and the media can also shape the Court's analysis and conclusions.
Once a case is accepted, briefs are submitted, presenting arguments and precedents. At times, amicus curiae briefs are also considered. After oral arguments and internal conferences where the justices discuss and vote in private, they reach a decision which is then made public.