The Borda Count, the Kemeny Rule, and the Permutahedron

A strict ranking of n items may profitably be viewed as a permutation of the objects. In particular, social preference functions may be viewed as having both input and output be such rankings (or possibly ties among several such rankings). A natural combinatorial object for studying such functions is the permutahedron, because pairwise comparisons are viewed as particularly important. In this paper, we use the representation theory of the symmetry group of the permutahedron to analyze a large class of such functions. Our most important result characterizes the Borda Count and the Kemeny Rule as members of a highly symmetric one-parameter family of social preference functions.