
Writ of mandamus is pretty much “we the court demand a different government official to perform your legal duties as they’re written and required.” Madison refused to give Marbury his court appointment, Supreme Court said this would be a great moment for a writ of mandamus but couldn’t perform it (was against a law or something). She was a legally and fairly elected official and her district is not currently being represented, his legal duty is to swear in new members of the House as Speaker