The Supreme Court would MOST LIKELY choose to hear Case 1.
Here are the reasons why:
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Case 1 involves the Fourteenth Amendment and has resulted in conflicting decisions from different US Circuit Courts of Appeals. This presents a significant legal question that may affect rights and protections for a minority group, and the Supreme Court often takes cases where there are differing interpretations of federal law among circuit courts to provide clarity and uniformity.
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Case 2 deals with a state law and its interpretation under the state constitution, which is generally less likely to attract Supreme Court attention unless it has broader implications or conflicts with federal law.
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Case 3 deals with a specific criminal procedure issue related to Fourth Amendment rights. While this could be relevant, the situation involves a lower court's decision on procedural matters that are less likely to have the broad impact the Supreme Court typically looks for.
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Case 4 is at an earlier stage, with no lower court's ruling available yet. The Supreme Court is typically more inclined to review cases that have undergone lower court proceedings to allow for established legal foundations and precedent.
Thus, in light of the importance of uniform interpretation of federal constitutional rights and the existence of conflicting lower court rulings, Case 1 is the most likely candidate for the Supreme Court to hear.