Discussions could start from less extreme positions if we had two things: (1) minds in the habit of being constructively critical and (2) ways to capture many, many opinions with minimal cost.

For #2, I think that a technological solution can be started on, though I admittedly have no idea what I want (or I would have started on it myself). The weakness of democracy, and the Internet, is that our tools for discussion are really, really weak. They do this thing where they're kinda-sorta paying lip service to real-time conversation... except that they're very much not. And they pay lip service to long-form discussion, except that no one really has the time, energy, or reason to properly parse an essay-length exploration of a subject.

This needs to change. Despite what Jeff Atwood seems to think, a better forum isn't really an answer: all that does is capture all the drawbacks of human conversation, notably the difficulty of acknowledging the many nuances in thousands of other opinions. Dozens, our human brains can manage on a good day and with some talent. Hundreds, thousands, millions, billions goes from silly to impossible. But we need to find a way to do it anyways.

For #1, that's a completely different solution.