If you seek an interesting example of applied random selection to democratic processes, have a look at France's "Citizens Convention for Climate" [1]. It was a panel of ~150 citizens chosen at random among the general population to think about what could be done to reduce France's carbon footprint, and make proposals that could be implemented into law.
From an environmental POV, this was absolutely useless as the government ignored most of their proposals in the end, but from an experimentation POV, it did demonstrate the viability of "citizens focus groups". In a few sessions over the course of about a year, those 150 random citizens got to meet with actual experts of climate science and french law, and became knowledgeable enough to make informed proposals that actually looked quite good.
[1] https://en.wikipedia.org/wiki/Citizens_Convention_for_Climat...