Switzerland

Switzerland runs a form of Direct Democracy. You can read about it here.

It's interesting to note that their form of direct democracy has evolved over many centuries, suggesting that it can work amongst a populace with a medieval level of education.

One of the distinctions of the Swiss system is that votes are carried only by a combination of an overall majority and a majority of cantons (similar to counties). This may be especially important in Switzerland where areas are clearly and dramatically divided by mountains, and would have been especially important in the olden days when mobility was so much harder.