by [12 7, 4, 3, 2, 1]. A weighted voting system (WVS) is described a) Which...

 

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by [12 7, 4, 3, 2, 1]. A weighted voting system (WVS) is described a) Which player is pivotal in the sequential coalition (7, 4, 2, 1, 3)? Show your work! b) Find the Shapley-Shubik power index of the smallest player with weight 1, in this WVS. No need to compute the whole power distribution. Hint. First think of winning coalitions which include the last player as critical in the Banzhaf sense. What would the total weight of such a coalition have to be, with and without the last player? (There is only one such winning coalition, eg {7, 3, 2, 1} is winning but 1 is not critical in it). by [12 7, 4, 3, 2, 1]. A weighted voting system (WVS) is described a) Which player is pivotal in the sequential coalition (7, 4, 2, 1, 3)? Show your work! b) Find the Shapley-Shubik power index of the smallest player with weight 1, in this WVS. No need to compute the whole power distribution. Hint. First think of winning coalitions which include the last player as critical in the Banzhaf sense. What would the total weight of such a coalition have to be, with and without the last player? (There is only one such winning coalition, eg {7, 3, 2, 1} is winning but 1 is not critical in it).