4 problems

Let $w_1,w_2,w_3, \ldots, w_m$ be positive weights, let $w$ be their maximum, and set … For a voting game with these weights, let $\beta_i$ denote the relative Banzhaf index of pla…

Inverse power index lower-bound conjecture. Every such simple game satisfies

Let $c_\mathcal{C}(n)$ denote the maximum critical threshold value of a complete simple game on $n$ voters. Complete-game growth conjecture. … This is the asymptotic form of the pa…

Let $c_\mathcal{S}(n)$ denote the maximum critical threshold value among simple games on $n$ voters. Simple-game threshold conjecture. For every $n\ge 4$, … The paper proves the di…