6 problems

For $n$ voters, the normalized Banzhaf power vectors of weighted majority games are points in the unit simplex. The interior of the unit simplex consists of normalized nonnegative…

For each $n\ge6$, define … A simple game is a monotone voting game on $n$ voters, and $\operatorname{Bz}(v)$ denotes its normalized Banzhaf power vector. Exact two-level Banzhaf co…

For each $n\ge2$, define … A weighted majority game is a game represented by a quota and nonnegative voter weights. Two-level Banzhaf lower-bound conjecture. There is a constant…

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. … T…

Let $W\subseteq\mathbb{R}_{\ge 0}$ be a set of weights, let $N^{(0)}\subsetneq N^{(1)}\subsetneq\dots$ be an infinite increasing chain of finite non-empty sets, and put…

Let $n_1,n_2$ be the numbers of players of the two types, and let $Bz_2(a,b,n_1,n_2)$ denote the relative Banzhaf power index of a player of type $2$ in the corresponding complete…