Personally, I am a strong sympathiser of democracy by sortition.
Historically, the main references to government by sortition refer to Classical Athens and the Florentine Republic in the Early Renaissance.
For those interested in the Florentine experience, in general less known to the public, here’s a great draft paper [pdf] by Yves Sintomer that he presented during a meeting we had a couple of years ago at the Rockefeller Center in Bellagio. In the paper, among other things, Yves describes the experience of the Florentine Republic and contrasts it with recent democratic innovations based on random selection. As to these recent experiments, alongside citizens’ juries, probably one of the most studied experiments with sortition in recent history refers to British Columbia’s Citizens’ Assembly on Electoral Reform.
At a time when citizen participation is considered – at least in theory – an important part of the open government movement, those working in this sphere should pay particular attention to different methods of participant selection (e.g. self-selection, randomized) and what the prospects and limits for each of these different methods are.
An awesome read on this subject is the book Democratic Innovations by Graham Smith. Among other things, Graham looks at the impact that different institutional designs (and methods of selection) have on the inclusiveness of participatory experiences.
If you are interested in sortition, a good resource to follow is the Equality by Log blog. In the blog I just came across an interesting presentation [PDF] by Yoram Gat on the subject of sortition compared to traditional (i.e. representative) democratic institutions.
Maybe after some of these readings you may become a sympathiser of government by lot as well.