That suggestion reminds of the system in Arthur C. Clarke's Imperial Earth:
“For the last century, almost all the top political appointments on Terra had been made by random computer selection from the pool of individuals who had the necessary qualifications. It had taken the human race several thousand years to realize that there were some jobs that should never be given to people who volunteered for them, especially if they showed too much enthusiasm. As one shrewd political commentator had remarked: “We want a President who has to be carried screaming and kicking into the White House – but will then do the best job he possibly can, so that he’ll get time off for good behavior.”
“For the last century, almost all the top political appointments on Terra had been made by random computer selection from the pool of individuals who had the necessary qualifications. It had taken the human race several thousand years to realize that there were some jobs that should never be given to people who volunteered for them, especially if they showed too much enthusiasm. As one shrewd political commentator had remarked: “We want a President who has to be carried screaming and kicking into the White House – but will then do the best job he possibly can, so that he’ll get time off for good behavior.”