Unstable Elections

Chefland is holding its first ever elections! Chefland is home to $N$ people (numbered $1$ to $N$), and there are $M$ candidates (numbered $1$ to $M$) standing for the elections. The election in Chefland follows a *ranked-choice* system. - First, each person must provide their order of preference of candidates, represented by a permutation$^\dagger$ of the integers $1$ to $M$, say $P = [P_1,