Weighted voting game (source code)

= Weighted voting game
{title2=$v(S)=1_{\{\sum_{i\in S}w_i>t\}}$}

A weighted voting game assigns player weights and a threshold, and declares <coalitions> winning when their total weight passes that threshold. The strict $>t$ convention is equivalent to quota $t+1$ for integer weights; another common convention writes a weak inequality directly. Nontrivial examples are <simple cooperative games>. Having nonnegative weights does not guarantee a <convex cooperative game>: two-of-three majority supplies a counterexample.