  The traditional methods of finding mixture components of rank data are mostly
based on distance and latent class models; these models may exhibit the
phenomenon of masking of groups of small sizes; probably due to the spherical
nature of rank data. Our approach diverges from the traditional methods; it is
directional and uses a logical principle, the law of contradiction. We discuss
the concept of a mixture for rank data essentially in terms of the notion of
global homogeneity of its group components. Local heterogeneities may appear
once the group components of the mixture have been discovered. This is done via
the exploratory analysis of rank data by taxicab correspondence analysis with
the nega coding: If the first factor is an affine function of the Borda count,
then we say that the rank data are globally homogenous, and local
heterogeneities may appear on the consequent factors; otherwise, the rank data
either are globally homogenous with outliers, or a mixture of globally
homogenous groups. Also we introduce a new coefficient of global homogeneity,
GHC. GHC is based on the first taxicab dispersion measure: it takes values
between 0 and 100\%, so it is easily interpretable. GHC measures the extent of
crossing of scores of voters between two or three blocks seriation of the items
where the Borda count statistic provides consensus ordering of the items on the
first axis. Examples are provided. Key words: Preferences; rankings; Borda
count; global homogeneity coefficient; nega coding; law of contradiction;
mixture; outliers; taxicab correspondence analysis; masking.
