Though "participatory democracy" sounds like "direct democracy", they are distinct.
]Further, by eliding deliberation, the initiative process is the worst kind of direct democracy. Except for mob rule, of course.
https://en.wikipedia.org/wiki/Participatory_democracy
The OP narrowly focuses on the calculus (?) of how randomly choosing reps actually promotes meritocracy.
This wiki article is a good overview of the whole burrito.