Dietrich Stoyan writes:

I asked the IMS people for an expert in statistics of voting/elections and they wrote me your name. I am a statistician, but never worked in the field voting/elections. It was my son-in-law who asked me for statistical theories in that field.

He posed in particular the following problem:

The aim of the voting is to come to a ranking of c candidates. Every vote is a permutation of these c candidates. The problem is to have probability distributions in the set of all permutations of c elements.

Are there theories for such distributions?

I should be very grateful for a fast answer with hints to literature. (I confess that I do not know your books.)

My reply: Rather than trying to model the ranks directly, I’d recommend modeling a latent continuous outcome which then implies a distribution on ranks, if the ranks are of interest. There are lots of distributions of c-dimensional continuous outcomes. In political science, the usual way to start is to model the positions of the candidates and of the voters, and then to have a model mapping relative positions to relative preferences.