Two Measures of the Dependence of Preferential Rankings on Categorical Variables

Abstract

Abstract. The aim of this paper is to apply a general methodology for constructing statistical methods, which is based on decision theory, to give a statistical description of preferential rankings, with a focus on the rankings' dependence on categorical variables. In the paper, I use functions of description errors that are based on the Kemeny and Hamming distances between preferential orderings, but the proposed methodology can also be applied to other methods of estimating description errors.Keywords: decision theory, individual preferential ordering (ranking), group (social) preferential ordering (ranking), Kemeny distance, Hamming distance, generalized regression, measure of the intensity of a dependence, computational complexity.