Much as the topic is close to my heart because of its importance, and the problems I see with current forms, I haven’t been able to follow this thread closely and so am not sure if this has been mentioned.
Sortition is an ancient (Greeks again) way of avoiding some of the problems of both direct and representative democracies, but has been used in contemporary settings too so there is good evidence about it (if you were to look, I assume). See here:
http://www.coopwatercooler.com/discussions//4m79q1m88fwktufew30pyeg3k4i9zh
Lots of good stuff like this appears in the excellent Facebook [spit] p2p group, which is where I found it.