The board of a football club consists of three extremely wealthy owners and five fans of the club. To decide on a proposal, the board uses a voting game in which all three wealthy owners and at least two fans must vote in favour in order for the proposal to be accepted. (a) Show that the voting game use by the board for deciding whether to approve a motion can be weighted. (b) For the voting game used by the board, find the Shapley-Shubik index of each fan. Hence, or otherwise, find the Shapley-Shubik index of each extremely wealthy owner. (c) Suppose that the board changes the voting game used to decided whether to ap- prove a proposal so that, in order to be approved, at least two extremely wealthy owners and at least three fans must vote in favour of the proposal. Can this voting game be weighted? Briefly justify your answer.

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