This would force people to vote for a candidate based on their own individual merits rather than just being part of a group.
Should the Democrat and Republican parties just shove off?
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No. A better solution, IMO, is to introduce ranked/preferential voting. It would serve to weaken the power of established parties and open politics to more perspectives, but that's also why the parties would not vote to implement it. There's also no guarantee that people would change their voting habits, but at least the opportunity would be there.