That ain't how it works. If the VP resigns, no one is "appointed" to the position, the Speaker of the House is moved into that slot... and they ain't gonna do THAT!
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“Trouble rather the tiger in his lair than the sage among his books. For to you kingdoms and their armies are things mighty and enduring, but to him they are but toys of the moment, to be overturned with the flick of a finger.”
― Gordon R. Dickson, Tactics of Mistake
― Gordon R. Dickson, Tactics of Mistake