Application of lower quantiles for complete lattices to ranking data: analyzing outlyingness of preference orderings

Abstract

The aim of the present paper is to apply a recently developed quantile approach for lattice-valued data to the special case of ranking data. We show how to analyze profiles of total orders by means of lattice-valued quantiles and thereby develop new methods of descriptive data analysis for ranking data beyond known methods like permutation polytopes or multidimensional scaling. We furthermore develop an aggregation rule for social profiles (, called commonality sharing, here,) that selects from a given profile that ordering(s) that is (are) most centered in the profile, where the notion of centrality and outlyingness are based on purely order-theoretic concepts. Finally, we sketch, how one can use the quantile approach to establish tests of model fit for statistical models of ranking data.