Here wi ge 0 are called weights and q gt 0 is called a

Question

Question: 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 q = 1/2 Σ_{i ε N} w_i . 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.