A simple majority vote of the justices who reviewed the case. Ideally, all nine justices would consider every case, but circumstances sometimes interfere with that.
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The requirements for the supreme court is to ensure they are following the constitution in all rulings.
The Supreme Court reviews the rulings of the lower Federal Courts. They hear cases that they grant certiorary to typically related to Constitutional law. Their rulings are the official Federal interpretation of the law.
The Judicial Branch
Do you want that answered by the way things are today or by the way the Foundersenvisioned? First, I'm not sure its the Supreme Court's job to "influence social policies". The duty of the Supreme Court is tointerruptlaw as declared by the U.S. Constitution.The strengths are the justice do not serve terms therefore they are not restricted by the ballot box and can vote as they see the law. The rulings of the Supreme Court are beyond appeal.The weakness is the Supreme Court depends on the President to enforce its rulings and Congress to ensure the president does it.
Whenever a U. S. President is in violation of the law as interpreted by the U. S. Supreme Court (or even if he/she is in violation of a law that the Supreme Court has not tested), it is the responsibility of Congress to impeach him/her.