Final answer:
Supreme Court justices discuss cases in a private conference and vote on decisions following oral arguments. They hear cases primarily through writs of certiorari and are guided by legal facts, precedent, and statutory law in their decision-making.
Step-by-step explanation:
Supreme Court justices follow a set process when deciding on a case. After oral arguments, justices convene in a private conference. The chief justice speaks first, followed by the others in descending seniority. An initial vote is cast in private. For a case to be heard, it usually arrives by way of a writ of certiorari, which requires the agreement of at least four justices. They only choose cases that present a constitutional issue or where different interpretations of law have occurred.
Their decision-making process involves consideration of legal and factual constraints, prior court precedents, the Constitution, and statutory laws. While courts are expected to be apolitical, there is debate on whether public opinion influences judicial review. Ultimately, the majority opinion, as well as dissenting or concurring opinions, form the Court's final decision, which is binding nationwide.