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Prove given game cannot represented as weighted majority

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Reference no: EM131333149

A projective game with seven players Consider a simple game with seven players, with winning coalitions:
{1, 2, 4},{2, 3, 5},{1, 3, 6},{3, 4, 7},{1, 5, 7},{2, 6, 7},{4, 5, 6},

and every coalition containing at least one of these winning coalitions. The game is presented graphically in the following figure. Each winning coalition must contain three players who are either all along one of the straight lines, or all on the circle.

540_figure.jpg

Prove that this game cannot be represented as a weighted majority game.

Reference no: EM131333149

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