  In the unidimensional unfolding model, given m objects in general position
there arise 1+m(m-1)/2 rankings. The set of rankings is called the ranking
pattern of the m given objects. By changing these m objects, we can generate
various ranking patterns. It is natural to ask how many ranking patterns can be
generated and what is the probability of each ranking pattern when the objects
are randomly chosen? These problems are studied by introducing a new type of
arrangement called mid-hyperplane arrangement and by counting cells in its
complement.
