So whoever gets the pick the secret list of experts gets all of the power.
Oh, that's easy! Just have a random panel of journeymen pick each expert, and random panels of novices pick the journeymen! Oh, and don't forget the random panel of complete idiots, who pick up the lunch orders!
I prefer this solution: politicians give up all privacy for political power, the penalty for corruption is as severe as the one for treason, and applies to those who give bribes, as well as those who receive bribes, and anyone who facilitates the process.