If your goal was to use a voting system that favored two party dominance and required leaders to pander to the extremes, you would use our current system. If your goal was to use a voting system that maximized voter expression, was biased towards none, ensured every candidate could be viable, and resulted in less pandering to the extremes, you would use score voting.
With score voting voters give each candidate a score between 0-9, they give a low score to candidates they like the least, and a high score to candidates they like the most. In the end the candidate with the most points still wins. Score voting is simple, competitive and fair (the Olympics use it), and because it has so many upsides and no downsides, I call it the silver bullet of reforms. With this one reform, everything changes, and for the better.
Republicans you say you like competition? Democrats you say you like fairness? Great, then you should both be supportive of this reform.