The problem with that is you effectively give partisans two votes: a strong approval for their guy and a strong disapproval of your guy. It's worth noting that

The problem with that is you effectively give partisans two votes: a strong approval for their guy and a strong disapproval of your guy. It's worth noting that there is a mathematical discipline of studying voting systems. Approval has been studied quite extensively and seems to have fewer flaws than most other methods—though it has been proven that no method can be perfect.