a) intelligence - an IQ of 100 simply isn't sufficient to know what to do about complex subjects, try starting at say 130 for national-level issues
b) knowledge - obviously you have to know what the hell you're talking about, which is kinda the whole point of the thread to here
c) conscientiousness - we don't need any evil geniuses running things, you have to want to be a good leader and do the right thing for the people under you.
mind you, before anyone says some bullshit about "well who gets to decide", this is the absolute baseline. regardless of what system is used to create this intellectual oligarchy (which wouldn't be that difficult to do fairly anyway imo) only someone with those qualifications has the potential to be a good leader at all except by accident or if acting as proxy for others'.
You will have many recoverable tape errors.