Uniform Banzhaf and Shapley–Shubik approximation lower bounds

For each $n\in\mathbb{N}$, let $\sigma^n=(0.75,0.25,0,\dots,0)\in\mathbb{R}_{\ge0}^n$, and let $v$ be a simple game on $n$ voters. Uniform approximation lower-bound conjecture.

$$\left\Vert\operatorname{Bz}(v)-\sigma^n\right\Vert_1\ge\frac{14}{37}\qquad\text{and}\qquad\left\Vert\operatorname{SSI}(v)-\sigma^n\right\Vert_1\ge\frac13.$$

These bounds concern non-approximability of a concentrated desired power distribution; the supplied text gives no resolution.