Question

Consider the weighted voting system [14:8, 6, 4]. Write down all the sequential coalitions and identify the pivotal player in each sequential coalition.

a) [P1, P2, P3], [P1, P3, P2], [P2, P1, P3], [P3, P1, P2]

b) [P1, P2, P3], [P1, P3, P2], [P2, P1, P3], [P2, P3, P1], [P3, P1, P2], [P3, P2, P1]

c) [P1, P2, P3], [P1, P3, P2], [P2, P1, P3], [P3, P1, P2], [P3, P2, P1]

d) [P1, P2, P3], [P1, P3, P2], [P2, P1, P3], [P2, P3, P1]

Answer 1

The correct answer is option c) [P1, P2, P3], [P1, P3, P2], [P2, P1, P3], [P3, P1, P2], [P3, P2, P1]. The pivotal player in each sequential coalition is P1 in the first two coalitions, P2 in one coalition, and P3 in two coalitions.

Step-by-step explanation:

The correct answer is option c) [P1, P2, P3], [P1, P3, P2], [P2, P1, P3], [P3, P1, P2], [P3, P2, P1].

In a weighted voting system, sequential coalitions are formed by considering different orders of the players in each coalition. The pivotal player in each sequential coalition is the player whose absence would result in the coalition losing its ability to achieve the required total weight to make decisions.

By examining all the sequential coalitions in option c), we can identify the pivotal player in each coalition:

• The pivotal player in [P1, P2, P3] is P1.
• The pivotal player in [P1, P3, P2] is P1.
• The pivotal player in [P2, P1, P3] is P2.
• The pivotal player in [P3, P1, P2] is P3.
• The pivotal player in [P3, P2, P1] is P3.