The technical term is sortition. And it is my pet unorthodox political position. The legislature should be replaced with an assembly of citizens picked by lottery.
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]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.