Alex, Becky and Carol are CEOs of three companies. They each have 41% voting rights in their companies. The remaining 59% is divided equally among the other board members. To implement a policy, the board requires to get a simple majority. If Alex’s board has five other members, Bcky’s six members and Carol’s seven, who among them is the most powerful CEO?
Let’s start with Alex: Each of his other members holds 59/5 = 11.8% control. So, if Alex manages to move one out of 5 towards him, he can change the policy (41 + 11.8 = 52.8 > 50). Becky also needs only one other member. So she has one in six chance to influence (41 + 9.83 = 50.83 > 50). So Becky has an easier job than Alex. Finally, Carol: one member (59/7 = 8.43) is not enough to make the majority. So, she needs two out of seven support which is harder than one in six. So Becky is more powerful.
