Ordinal Unfolding of Preference Rankings using the Kemeny Distance

Multidimensional unfolding can be seen as a special case of Multidimensional Scaling (MDS) with two sets of points, in which the within sets proximities are missing. Lack of the within‐sets information is the major cause of well‐known problems of degenerate solutions in analytical procedures, especially for ordinal (or non‐metric) unfolding. Over the years, several approaches to avoid degenerate solutions in unfolding have been developed. Our approach belongs to the category of methods that aim to extend the unfolding data with information on the dissimilarities between rankings (Van Deun et al, 2007). By starting from a typical rectangular matrix, in which each row is a preference ranking, we propose a reconstruction strategy of the entire dissimilarity matrix based on the properties of the Kemeny distance (Kemeny and Snell, 1962) and the τ_X extended rank correlation coefficient (Emond and Mason, 2002). We show that our unfolding procedure can be used with any standard MDS program and produces non‐ degenerate solutions. These solutions are simple to compute, while comparable in quality with the ones returned by the PREFSCAL algorithm (Busing, Groenen and Heiser, 2005), currently the state‐of‐the‐art method for avoiding degeneracies in unfolding.