Best not to overthink think. It’s the best random number generator they thought they had. Even ours suck.
They just wanted a member of the Aristocrat to be in charge is the point. An inauguration validated with whatever appears like merit (but the whole thing is rigged since only one type can ever win - the aristocrat (the entire pool is aristocrats)).
When they say “reduced by lot” then mean by a lottery? By that same original boy or something else?
They also talked about needing approval from electors, I assume that was from the previous small pool. Can’t exactly determine who they mean.