Assume $m$ independent binary classifiers with probability $p$ to be correct $p>0.5$. Show that the probability of a voting, e.g. decision is made by the majority of classifiers is correct with probability $q>p$.
I think this problem as equivalent to showing that the Binomial cumulative distribution $\text{CDF}(k,n,p)$ follows $\text{CDF}(k=m/2, m, p) < 1-p$
$z=\sum_i{x_i}\text{ ; } \Pr(C)=\Pr(z>m/2)\\ \text{Markov's Inequality: } \Pr(X\geq a)\leq {\frac {\mathbb {E} (X)}{a}}.\\ \text{define } y=m-z \text{ then } Pr(\epsilon)=\Pr(y\ge m/2)\le \frac{m(1-p)}{m/2}=1/2(1-p)\\ \Pr(C)=1-\Pr(\epsilon)>(p+1)/2>p$