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Up until the Jefferson administration the US vice-president was not the president's running mate. He was the runner up. After John Adams was elected his vice-president was Jefferson since he was the runner up. Same can be seen in the election of 1800 too as Aaron Burr became Jefferson's vice-president because he was the runner up (they actually received the same vote so the congress decided who won). So the question is what if this system stayed. It could have very interesting consequences.