Given the weighted voting system [6: 4, 3, 2, 1], which of the coalitions listed are minimal winning coalitions?
$$\text { I } \{ A , B \} \quad \text { II } \{ A , C \} \quad \text { III } \{ B , C , D \}$$
A) I only
B) I and II
C) II and III
D) I, II, and III

Question

Given the weighted voting system [6: 4, 3, 2, 1], which of the coalitions listed are minimal winning coalitions? 
$$\text { I } \{ A , B \} \quad \text { II } \{ A , C \} \quad \text { III } \{ B , C , D \}$$
A) I only
B) I and II
C) II and III
D) I, II, and III

Quizplus · Accepted Answer

In a weighted voting system, a coalition is considered a minimal winning coalition if it has enough votes to meet or exceed the quota (in this case, 6) and removing any member would cause the coalition to no longer meet the quota. All three coalitions listed meet these criteria: Coalition I (A, B) has 7 votes, Coalition II (A, C) has 6 votes, and Coalition III (B, C, D) also has 6 votes. Removing any member from these coalitions would drop the vote total below the quota, making all of them minimal winning coalitions.

Given the Weighted Voting System [6: 4, 3, 2, 1] I {A,B} II {A,C} III {B,C,D}\text { I } \{ A , B \} \quad \text { II } \{ A , C \} \quad \text { III } \{ B , C , D \} I {A,B} II {A,C} III {B,C,D}

Given the Weighted Voting System [6: 4, 3, 2, 1] $\text { I } \{ A , B \} \quad \text { II } \{ A , C \} \quad \text { III } \{ B , C , D \}$