Final answer:
In the case of Marbury v. Madison, the Supreme Court ruled in favor of James Madison, while simultaneously establishing the principle of judicial review, which allows the Court to declare laws unconstitutional.
Step-by-step explanation:
In the landmark case of Marbury v. Madison (1803), the Supreme Court issued a decision that James Madison won, because even though the court recognized William Marbury's right to his commission, it did not have the power to issue a writ of mandamus to enforce it.
The judgment was made by Chief Justice John Marshall, who found that the Judiciary Act of 1789, which conferred upon the Court the power to issue such a writ, was in fact unconstitutional.
This was because it extended the Court's original jurisdiction beyond what Article III of the Constitution allowed.
As a result, Marbury did not get his commission, but the case became the cornerstone for the establishment of the principle of judicial review, where the Supreme Court reserves the right to invalidate legislation that it finds conflicts with the Constitution.