Question

Use the weighted voting system: [15: 9, 8, 7] to answer the following questions. If the coalition is a losing coalition, mark "this is a losing coalition" If the coalition is a winning coalition, identify the critical players. Question 1 The critical players in [P₁] are P₁ ☐ P₂ 1 P3 This is a losing coalition, so there are no critical players This is a winning coalition, but there are no critical players Question 2 The critical players in [P2] are O P1 P2 P3 This is a losing coalition, so there are no critical players This is a winning coalition, but there are no critical players 1

Answer 1

Based on the given information, we can determine if each coalition is a winning or losing coalition by comparing the total weight of the coalition to the quota, which is calculated as (total weight / 2) + 1.

For example, in the coalition [P₁], the total weight is 15, and the quota is (15 / 2) + 1 = 8.5, which rounds up to 9. Since the total weight of the coalition is less than the quota, [P₁] is a losing coalition.

Similarly, we can determine that [P2] is a winning coalition because its total weight is 9, which is greater than the quota of 8.5.

Since [P₁] is a losing coalition, there are no critical players in that coalition. Similarly, there are no critical players in [P2] since every player has enough weight to make the coalition winning.

Therefore, the answers to the given questions are:

Question 1: This is a losing coalition, so there are no critical players. Question 2: The critical players in [P2] are P₁, P₂, and P₃.

Explanation: