The chair of a decision-making body has special responsibilities and often has special voting privileges. In some cases, these privileges give the chair more power than other members. We next look at slightly different scenarios to examine how the size of the committee and the nature of the chair’s vote relate to power.
a. A committee consists of five members: the chair and four other members. Each of the four other members has equal weight. The committee rules call for a simple majority, but the chair votes only if there is a tie. In the case of a tie, the chair casts the deciding vote. Find the Banzhaf power index for each member of this committee.
b. A committee has four members: the chair and three other members. Each of the three other members has equal weight. The committee rules call for a simple majority, but in the case of a tie, the coalition that includes the chair wins. Find the Banzhaf power index for each member of this committee.
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