> The median position of a bunch of half-informed individuals plied with advertising is not something I have a lot of confidence in.

And here lies the problem. In the US the 1% actively disinforms the 99% through media manipulation and bad education. Thus you can't have direct democracy when people can't think for themselves. The whole system is rotten.

In most European countries citizens are educated from a young age how to think rationally and how to interpret information. You still have subtle media manipulation like sky-news but nothing as blatant as fox-news&hollywood. Switzerland has a very good history of referenda - because the population isn't intentionally misinformed and under-educated.