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Voting System

13. An executive board consists of a president (P) and three vice-presidents (V1,V2,V3)(V1,V2,V3). For a motion to pass it must have yes votes from three of the voting members, one of which must be the president’s.

A weighted system that could represent this situation is:


QQ =
PP =
V1V1 =
V2V2 =
V3V3 =

12. Consider the weighted voting system [12: 7, 4, 1]

Find the Shapley-Shubik power distribution of this weighted voting system.

List the power for each player as a fraction:

11. Consider the weighted voting system [15: 14, 6, 4, 1]

In the sequential coalition which player is pivotal?

Pivotal player =

Identify players by their number only. For example, if the answer is P2P2, enter 2