Solution
= Solution
\b[False.] Take three players of weight one and strict threshold one, so a <coalition> wins exactly when it contains at least two players. Set $S=\{1,2\}$ and $T=\{2,3\}$. Then
$$
v(S)=v(T)=v(S\cup T)=1,\qquad v(S\cap T)=v(\{2\})=0.
$$
The <convex cooperative game> inequality would require $1\ge1+1-0=2$. Thus even this elementary majority <weighted voting game> is not convex.