In the weighted voting system below, the weights represent voters \( A, B, C \), and so on, in that order. Find the critical voter(s) in the winning coalitions. \( [14: 1,4,6,8] \) In all the winning coalitions \( \{C, D\},\{A, C, D\},\{B, C, D\} \), and \( \{A, B, C, D\} \), who is(are) the critical voter(s)? A and B C and D D C
Solución de tutoría real
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Solución
Revisado y aprobado por el equipo de tutoría de UpStudy
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The Deep Dive
In the weighted voting system \( [14: 1,4,6,8] \), a critical voter is one whose vote is essential for a coalition to achieve the total weight of 14 votes needed to win. In the specified winning coalitions, let's analyze each: 1. For coalition \( \{C, D\} \), C is critical because without C's 6 votes, they cannot reach the total. 2. For coalition \( \{A, C, D\} \), A is the critical voter; without A's 1 vote, the coalition only reaches 14. 3. In \( \{B, C, D\} \), B is critical because without B's 4 votes, they cannot reach the target. 4. Lastly, in \( \{A, B, C, D\} \), A and B are both critical as their votes play an essential role to achieve 14. So the critical voters collectively are A, B, and C through different coalitions.
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