> But raw approval gives undue advantage to moderates.

If by "moderates" you mean "most liked" then I'm not sure what the problem is here. The point of voting is to find the most universally agreed upon ruler. You may call this unfair, but I would say that it is MORE unfair to give advantage to fringe groups rather than giving advantage to the masses. I thought the point of democracies was about having rule by the masses. If you think fringe groups should have the advantage I'd like to hear your argument.

> I think (without data, happy to be proven wrong) that the US population is fairly strongly bimodal on most issues. Many issues that people care a lot about (for better or worse...) have two clear centers of gravity,

We'll you'll be happy then! :)

Because this is commonly believed but actually totally untrue. There's an entire book about it, "Culture War? The Myth of a Polarized America" by Morris P. Fiorina.

The upshot is basically that if you ask people binary yes/no questions (or binary left/right votes), the population appears divided, bimodal. But whenever you give a sliding scale in surveys, it becomes abundantly clear that the population is centrist -- unimodal. Even for gun control and abortion, the most hot-button issues.

If centrist is defined by the minimization of distance between a population's preference and a candidate's position then I don't see the problem. Why would you want an extremist? Or why would you want someone that is less representative of the population as a whole? Isn't the point of democracy to minimize this distance?

I'd actually argue that if approval was used Bernie would have won. One can vote Bernie honestly but also approve of Hillary as a safety. And this would have had a larger edge with Score or STAR. Bernie was quite popular and frankly a lot of people that also voted Trump also liked Bernie because he was an outsider.