value v(L) = 0 that is closed under taking subsets and a set W of winning coalitions W with v(W) = 1. Simple games with α … = minp>0 maxW∈W,L∈L p(L) p(W) < 1 are exactly the weighted voting games. We show that α 6 1 4n for every simple game (N …,v), confi rming the conjecture of Freixas and Kurz (IJGT, 2014). For complete simple games, Freixas and Kurz conjectured that α …