you have chosen an ass.
— The words of James Fournier, after his unanimous election in 1334 as Pope (Benedict XII). Whether he meant to be humble or ironic (or perhaps simply honest) is unclear.
Imagine there is a group of N people who wish to elect one of themselves as leader of the group. Each member of the group casts a vote, in a sequence of secret ballots, until one of them receives at least M votes. Two historically interesting examples of this situation are the so-called Imperial Election problem1 (N