When my children needed to divide a treat the younger ones always seemed to come up second best until I came up with this very simple solution: the oldest divides and then they all choose from youngest to oldest.
Bob is the oldest and wisest. Give him a day to divide up the cabinet posts into two teams. Head of the one team is president, head of the other is prime minister; then let Morgan have first choice of team on the second day. On the third day they all go home and start putting this poor, poor country back together again and save a few million (real money) in conference costs.