5 problems

Lower-bound optimality conjecture. If $\alpha \geq \frac{2}{k+1}$, then an $\alpha$-undominated set of size $k$ always exists.

Let $m^{(n)}$ be a sequence of weight distributions with corresponding probability distributions $(P^{(n)})_{n \in \mathbb{N}}$, where $P^{(n)}=(p_i^{(n)})_{i \in \mathbb{N}}$ is a…

Prime-multiple power-index conjecture. The divisors of the divisor voting systems of $pn$ and $mn$ have the same Shapley–Shubik power indices and the same Banzhaf power indices.

ADO optimality conjecture. For any fixed set of an odd number of distinct abilities for a jury, the ordering that produces the highest reliability is the ADO.

The Condorcet generating-function conjecture. (i) The series $B(x,P)$ converges for $0\leq x<\frac12$ and $x\leq P\leq\frac12$; (ii) $B(x,P)\geq 0$ on the same region; and (iii)