Martin v. Hunter's Lessee
Defendant was given his estate from Lord Fairfax, a British man who owned large of amounts of land in Virginia. Virginia had seized his land however based on a state law and sold part to plaintiff, who seeks to evict defendant. The Commonwealth's seizure was potentially in violation of international treaties however.
Trial court found for defendant.
Supreme Court of Appeals reversed.
Supreme Court of the United States reversed again, and remanded to the Virginia courts for them to enter judgment for defendant.
The Virginia Supreme Court refused to enter judgment for defendant, claiming that the US Supreme Court had no authority over it as it was of a different sovereign.
Can the US Supreme Court overrule state Supreme Courts?
Congress can vest as much power in the federal courts as the Constitution allows it to. Appellate jurisdiction allows courts to handle almost every case enumerated in the Constitution. Appellate power is also not limited by Article III to any particular courts. The cases give the jurisdiction, not the courts. If the Constitution limited the appellate courts' power to only be for federal cases, then it would have to be exclusive of the state courts because its jurisdiction extends to all cases arising under the constitution, laws, and treaties of the United States; or to all admiralty cases. If a state were to handle one of these, then the federal government would not have appellate power and would be limited to some of, not all cases where it was enumerated. Congress also could have not established lower courts, in which case the Supreme Court would not have any appellate cases to review if it could not review states'.
Article Six also requires judges to decide according to the constitution, laws, and treaties of the United States, not just according to their own states' laws. These federal issues will arise in state courts, but the Constitution delegates them to federal courts. If the courts have exclusive original jurisdiction, then the federal courts must have appellate jurisdiction over them. This is assumedly intended as it restrains states in many other places as well. This does not impair states' independence, as the very need for federal courts to review state courts implies their independence. All systems are open to abuse, and this is not extraordinarily so.
Leaving the entirety of the power with the state courts is also dangerous. The founders foresaw this when drafting the Constitution. Even though state judges are qualified and have good judgment as well, they will always get things wrong. They may also be biased due to their states' unique situations and give rulings unjust to people not from that state. This would also lead to differences between states on federal statutes and the Constitution, which would have disastrous consequences.
In addition, the Supreme Court has decided state cases before without states complaining.
The US Supreme Court has appellate jurisdiction over all state court cases.