Interesting. I'm not sure that random selection would be effective though - just look at the jury system, where the opinion of the relatively domain-uninformed body is manipulated by domain experts to attempt to reach the outcome that they desire. The same sort of thing would happen (IMO) in a political body -- the "shadow" government (i.e. the career government workers) would end up manipulating members of the body to a greater or lesser extent.
> the "shadow" government (i.e. the career government workers) would end up manipulating members of the body to a greater or lesser extent.
Certainly a risk, but we have already have a similar shadow government of congressional aids and special interest lobbyists today. I think this can be mitigated to some degree by providing funding and resources for self education, but this is something that would need to be taken under consideration as the system was designed and measured as the system was implemented.