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Simple games with $\\alpha= \\min_{p\\geq 0}\\max_{W\\in {\\cal W}, L\\in {\\cal L}} \\frac{p(L)}{p(W)}<1$ are exactly the weighted voting games. We show that $\\alpha\\leq \\frac{1}{4}n$ for every simple game $(N,v)$, confirming the conjecture of Freixas and Kurz (IJGT, 2014). 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