A weighted majority game has a characteristic function of the form Here, wi ≥ 0 are called…

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A weighted majority game has a characteristic function of the form

Here, wi ≥ 0 are called weights and q > 0 is called a quota. Take . Suppose that there is one large group with two-fifths of the votes and two equal-sized groups with three-tenths of the vote each. (a) Find the characteristic function. (b) Find the core and the least core.

(a) Find the characteristic function.

(b) Find the core and the least core