4 problems

Extremum-count conjecture. For every $k=1,\ldots,n$, the function $q\mapsto\mathbb{E}({\Greekmath 010C}_k^{\downarrow})$ has exactly $k-1$ local extrema on $(1/2,1)$.

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…

Let an Alon–Edelman type result mean a bound showing that a simple game's power vector is close to the power vector of a game with only the concentrated $k$ voters and the remainin…

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