6 problems

Continuous cutting-stock bound. For any weighted game $(N,\mathcal{W})$ on $n$ players,

Let $\operatorname{Nak}^{\mathcal{T}}(n,t)$ denote the maximum possible Nakamura number among weighted games on $n$ players with $t$ types of players, where $t\in\mathbb{N}_{>0}$.…

Let $n\ge 2$, let $\mathfrak{W}$ denote the class of weighted games, and let $c_{\mathcal{P}}(n,\mathfrak{W})$ be the cost of local monotonicity for the power-index collection…

Classification conjecture. Each type composition $\widehat{n}$ is either weighted or there exists a type composition $\widehat{m}$ in this list with $\widehat{n}\ge\widehat{m}$. Th…

Maximum-representation conjecture. For a given $t$, every weighted game can have at most $t-2$ different minimum sum representations preserving types, and this bound is tight.

A system of $n$ weights is a collection of $n$ weights, and satisfying the $n'$th Fishburn condition means meeting the combinatorial condition defined earlier in the paper. Fishbur…