Norbert Ohlenbusch alerted me to the existence of an extraordinary talk by psychologist Jonathan Haidt. It's less than 20 minutes long; I highly recommend it. It provides a very useful vocabulary that both ends of the political spectrum can use to understand why people can hold positions other than theirs and still claim the moral high ground.
The first few minutes can be rough going if you're a conservative; the live audience is mostly liberal, and so Haidt caters to that with a few cheap shots. But once he gets going, the substance of the talk is extremely valuable to thinkers on both sides.
The fact that people are doing research on this sort of thing gives me hope that we might someday be able to push the competitive mindset out of politics and replace it with something better.