Closest Ranking

You have just begun his job with Educated Guessing Pollsters. An election is only weeks away and the company would like to get a general idea of how the voters feel about the candidates. They asked a (probably not) random subset of N voters to submit a ranking of the M candidates. Say the candidates are numbered from 1 to M. A ranking is then a permutation of the set {1,2,...,M} listed as: c_1 c_