Exact cost of local monotonicity for the Banzhaf and proportional power indices

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 $\mathcal{P}=\left(\operatorname{Bz}^r,\operatorname{PGI}^r\right)$. Exact-cost conjecture.

$$c_{\mathcal{P}}(n,\mathfrak{W})=\max\!\left(0,\frac{n-3}{n-1}\right).$$

The preceding lower-bound result establishes the right-hand side as a lower bound, and the paper reports that it is attained computationally for all $n\le 10$. The conjecture concerns whether this lower bound is exact for every number of players; resolving it would determine the precise asymptotic cost of enforcing local monotonicity for this pair of indices.